Stock Prediction and Trading from OHLCV Data: A Quantum- Enhanced Learning-Based Comparison

Stock Prediction and Trading from OHLCV Data: A Quantum- Enhanced Learning-Based Comparison | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Stock Prediction and Trading from OHLCV Data: A Quantum- Enhanced Learning-Based Comparison Pratham Shah, Kshitij Shah, Tvisha Vedant, Vatsal Shah, Varshapriya Jyotinagar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9653068/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Stock price prediction remains a hard problem because financial time series are noisy, non-stationary and nonlinear. Although the literature is large, no single learning paradigm has shown sustained superiority across market regimes. We present a unified comparison of classical machine learning, deep learning, deep reinforcement learning and quantum machine learning on stock prediction and trading from OHLCV data, with greater emphasis on quantum models. Decision Tree, Ridge regression and Gradient Boosting are first developed; the comparison is then extended to Artificial Neural Network (ANN) and Long Short-Term Memory (LSTM). A Deep Q-Network (DQN) trading agent is also implemented. The same models are then re-implemented on variational quantum circuits, giving rise to Quantum Neural Network (QNN), Quantum LSTM (QLSTM) and Quantum DQN (QDQN). All models are trained and evaluated on the same dataset of 209,498 one-minute bars and approximately 27,500 daily bars across eleven liquid U.S. equities, under an identical leakage-free feature pipeline. Evaluation uses RMSE, MAE, directional accuracy, cumulative return and Sharpe ratio. On one-minute intraday data, returns are largely indistinguishable from a near-random walk and no model beats the naive baseline. On the daily horizon, deep learning models show small but consistent improvements; the quantum models perform comparably to classical counterparts at a fraction of the parameter count. The classical DQN delivers a positive average return across tickers, while the buy-and-hold strategy and the QDQN agent under-perform. Overall, near-term variational quantum circuits do not deliver a clear quantum advantage on this task, and careful experimental design matters more than model exoticness. Quantum machine learning Variational quantum circuits Stock price prediction Deep reinforcement learning LSTM OHLCV data Figures Figure 1 Figure 2 Figure 3 Figure 5 Figure 6 1 Introduction The financial markets play a vital role in today's economy and their roles include investment, capital allocation, and risk management. Hence, stock price forecasting is of immense importance for academics, traders, and many other financial institutions. An accurate forecast, even by a very little difference, will help to make optimal allocation of portfolio, intelligent trading and other financial decisions. Despite that, stock market forecasting is of very challenging nature because of the characteristics of the financial data. The characteristics of financial time series are different from majority of structured datasets used in machine learning applications. They exhibit strong volatility, non-stationarity and very noisy behaviour ( Kang 2025 ). Market trends are influenced by many macro-economic, geopolitical and various unpredictable factors. They influence time series in a nonlinear manner. Most early research regarding financial forecasting was done using classical statistical methods such as ARIMA and GARCH ( Fattah et al. 2018 ; Marisetty 2024 ) and these models inherently assume stationarity and linear relationships of the underlying time series. They are interpretable and have a theoretical foundation, but do not perform well for complex nonlinear relationships ( Atesongun and Gulsen 2024 ). Thanks to the growth of computing power and large amounts of historical data, the topic has shifted towards machine learning ( Wang et al. 2021 ). In the recent time, deep learning models such as Recurrent Neural Networks and Long Short-Term Memory (LSTM) ( Moghar and Hamiche 2020 ; Staudemeyer and Morris 2019 ) have yielded very promising results on sequence-based prediction tasks. At the same time, reinforcement learning (RL) has also been proposed as a trading framework ( Pricope 2021 ; Ghasemi and Ebrahimi 2024 ). Unlike supervised methods where the task is to predict price, RL can be defined as a sequence of decision-making tasks aiming at maximizing the long-term reward. The appearance of NISQ hardware has also expanded the prospect of QML for financial prediction ( Srivastava et al. 2023 ; Doosti et al. 2024 ); VQCs can be interpreted as differentiable layers within classical neural networks ( Beer 2022 ; Qi et al. 2024 ), and these have been proposed to offer an inductive bias that cannot be simulated with classical methods. Despite the abundance of research conducted on each of the methods above, few direct comparative studies between the four learning paradigms are conducted on a level playing field. Studies in the existing literature vary in dataset, feature preprocessing pipeline and metric used. This paper aims to fill in that void by introducing a standardized methodology for training and evaluating traditional machine learning models, deep learning models, deep reinforcement learning agents and their quantum-enhanced counterparts. Training and testing is performed on the same dataset, using the same leakage-free feature pipeline and the same time-chronological train/test split. Emphasis is placed on the quantum family of models — QNN, QLSTM, and QDQN — and on identifying when they might outperform their classical counterparts and when they do not, across different time frames (1-minute, 5-minute and daily). Key contributions of this paper are: (i) an equal empirical study of nine distinct models spanning all four learning paradigms on the same data; (ii) a rigorous methodology write-up detailing the essential adjustments that must be made to yield reliable results, most notably a gradient-flow correction applied to the hybrid PennyLane–PyTorch models; and (iii) a study of the models across various time horizons to reveal dependence of model superiority on data horizons. 2 Technical Overview Stock market prediction has been studied extensively in many sub-fields of statistics, machine learning, deep learning, reinforcement learning and, more recently, quantum machine learning. Over the years the research has progressed from simple statistical methods towards more complex data-driven and learning-based approaches. The early studies were based on statistical methods such as ARIMA and GARCH ( Fattah et al. 2018 ; Marisetty 2024 ; Groenendijk 2021 ). These methods are designed to capture temporal dependencies in the data and they work reasonably well on relatively stable and stationary series. They are also interpretable, which is desirable for financial decision-making. However, the assumptions on which these methods are built are rarely satisfied in real markets, where the underlying regime can change, volatility can shift abruptly and external economic events can introduce sharp non-linearities ( Atesongun and Gulsen 2024 ). After the emergence of higher computational resources, classical machine learning algorithms such as Linear Regression, Decision Tree and Random Forest were applied to the stock prediction problem ( Antad et al. 2023 ; Kumari and Yadav 2018 ; Fabiha et al. 2025 ; Jijo and Abdulazeez 2021 ; Rokach and Maimon 2005 ; Wu 2023 ). Among these, the Random Forest algorithm received considerable attention because of its ability to reduce variance through ensembling ( Cutler et al. 2011 ; Jadama and Toray 2024 ; Salman et al. 2024 ). Gradient boosted tree methods such as XGBoost have also been shown to be competitive on related tasks ( Chen and Guestrin 2016 ). However, classical machine learning models cannot easily model the long-range temporal dependencies in the data, and their performance is highly dependent on the quality of the engineered features. Artificial Neural Networks (ANNs) and Long Short-Term Memory (LSTM) networks helped to overcome some of these limitations. ANN-based feed-forward models were among the first deep learning techniques used for financial forecasting and they have been shown to capture nonlinear patterns better than classical models ( Grossi and Buscema 2008 ; Wen 2024 ; Ingle and Deshmukh 2021 ). LSTMs went a step further and provided an explicit mechanism for retaining memory, which makes them suitable for stock price prediction ( Moghar and Hamiche 2020 ; Chaudhary 2025 ; Ravina and Shrivastav 2025 ). Other recurrent variants such as the GRU ( Dey and Salem 2017 ) and attention-based models such as the Transformer ( Vaswani et al. 2017 ) have also been compared on similar problems ( Xiao et al. 2024 ). Simultaneously to research in predictive modeling, the concept of using reinforcement learning (RL) in financial trading has been explored as another alternative paradigm ( Pricope 2021 ; Ghasemi and Ebrahimi 2024 ). An RL setup represents financial trading as a sequence of decision-making actions performed by an agent within a market environment, with the possible actions being to buy, sell or hold, and a reward associated with the resulting portfolio value change. The Deep Q-Network (DQN) algorithm ( Mnih et al. 2013 ) has been proposed in the context of such tasks by enabling approximate learning of the value function in high-dimensional situations using deep neural networks. More recent extensions have looked into risk-sensitive rewards ( Sun et al. 2022 ), more complex state representations ( Goluza et al. 2024 ), or the explicit modelling of transaction costs. A much newer paradigm has emerged as quantum machine learning (QML) ( Srivastava et al. 2023 ; Doosti et al. 2024 ; Qi et al. 2024 ). The general structure used to date for QML-based financial prediction is to wrap a small, parametrised quantum circuit into a classical neural network and train the hybrid network end-to-end. Specifically Quantum Neural Networks (QNN) ( Beer 2022 ; Choudhary et al. 2025 ; Bathala et al. 2025 ), Quantum LSTMs (QLSTM) ( Chen et al. 2020 ; Kea et al. 2024 ; Su and Li 2025 ) and Quantum Reinforcement Learning agents (QRL/QDQN) ( Dong et al. 2008 ; Jerbi et al. 2021 ) have been proposed in the literature as quantum equivalents to the already existing ML, DL and RL models. It is believed that using a quantum circuit may increase the richness of feature representations through superposition and entanglement. However, the practical use of these methods raises issues. First, gradient signals can silently get “broken” at the quantum component, i.e., lost, when there is an issue with the framework's plumbing code. In this case apparent training of the quantum model happens while, in fact, only a classical model with frozen random projection is trained. Second, simulation of the quantum computation cost can grow very quickly with number of qubits and circuit depth; this limits the sizes of the problem that can be explored. However, applying frameworks such as Qiskit ( Javadi-Abhari et al. 2024 ) or PennyLane ( Shapiro 2025 ) allows applied researchers to perform experiments of this kind increasingly easily. An aspect that is pointed out repeatedly in all the reviews of the area is the lack of a single best model; the outcome depends on a number of factors, among them quality of data, feature engineering and market regime. Several pitfalls are also identified in the literature: models are prone to overfitting, i.e., their performance on training data fails to generalize; there is often no agreement on the methodology of experimental tests, thus hindering comparisons between studies; most predictive models are not adapted into a trading strategy; few RL approaches include comparisons with predictive models. Models for the different paradigms are generally analyzed separately, if at all. The motivation of this paper is the lack of unity pointed out in those papers; the goal is to present a comprehensive comparison of all the four paradigms, ML, DL, RL and QML within a unified framework. 3 Methodology In view of the lacunae indicated above, the methodology of the work carried out in this paper is designed in a principled and experimental manner so that impartial and reproducible comparisons between the four learning paradigms are possible. Whereas the vast majority of the published research concerning stock prediction and trading utilizes independent models and varying experimental settings, the work herein is aimed at utilizing the same datasets with the same chronological train/test split for all the four model categories. Since financial time series data are non-stationary, noisy and often incorporate complex non-linear relationships, the methodology goes beyond pure predictive accuracy and instead also compares the models in a simulated trading environment. Significant focus is dedicated to the quantum-domain models — QNN, QLSTM and QDQN — as well as on the practical difficulties encountered during the implementation of such models. The well-established classical machine learning, deep learning and reinforcement learning based methods are maintained as benchmarks and principled baselines to establish any purported advantages from quantum approaches against established concepts. This methodology consists of five main stages: design of the research, data specification, pre-processing and feature engineering, implementation across several time-scales (1 minute, 5 minute and daily), and evaluation. Each stage is detailed in the ensuing subsections. 3.1 Research Design The research design followed in this work is experiment-driven and focuses on enabling fair comparisons between the four learning paradigms investigated. All models are trained and tested over the same dataset and on the same 80/20 chronological split. The same set of lagged features is used wherever possible as input, the same metrics are used for evaluation, and significant care has been taken to eliminate potential forms of data leakage. The workflow consists of five stages: data description, data preprocessing and feature engineering, model implementation across timeframes, evaluation protocol, and analysis of the results. For describing implementation details, emphasis has been placed on quantum-domain models in line with the main direction of this research. 3.2 Data Description The historical stock data used throughout this work are presented in the conventional OHLCV (Open–High–Low–Close–Volume) format ( Kang 2025 ), standard in quantitative finance. Each record represents the overall movement of price over a period, accompanied by the traded volume. The data used comprise eleven large-cap U.S. equities — AAPL, AMZN, DIS, GOOGL, IBM, KO, META, MSFT, NVDA, SBUX and TSLA. Two different levels of granularities of the same dataset have been explored. The intraday dataset consists of 209,498 one-minute bars (a 5-minute aggregated version has been further examined), whereas the daily dataset contains about 27,500 daily bars corresponding to the same tickers. The selection of liquid large-cap equities minimizes the influence of possible illiquid events. The intraday data serves as a useful evaluation ground on a low signal-to-noise data problem, whereas the daily data contains smoother trends and is closer to the regime where other research has performed analyses ( Wang et al. 2021 ; Chaudhary 2025 ). The dataset spans across different market phases, i.e., bullish, bearish and sideway states, and this ensures that the comparison is relevant. The chronological 80/20 split ( Hasanov et al. 2022 ) ensures that time ordering is maintained. There are a number of known statistical properties of financial time series that guide the modelling. They are non-stationary (moments vary over time), and exhibit volatility clustering (high volatility episodes tend to follow high volatility). Return distributions are fat-tailed (extreme events are more probable than under a normal distribution). These properties motivate both non-linear sequential models and the use of reinforcement learning where the states can be adjusted via continuous interaction with the environment. 3.3 Data Preprocessing and Feature Engineering The preprocessing is carried out chronologically to maintain the time-series structure. Missing values are filled with interpolated values according to gap patterns. Outliers (mostly caused by anomalous trading events) are clipped to statistically computed moving bounds. Feature engineering — the most crucial part of the pipeline — is designed to avoid same-bar leakage, which is an important pitfall when predicting based on OHLCV data. If close or return on bar t is predicted using OHLCV on the same bar t, then the low and high, by construction, enclose the close. This would result in artificially high R² values, and an inaccurate model for future trading. This is avoided by only using lagged data. At time t we compute five lagged values (t − 1 to t − 5) of close, volume, and simple percentage return. Rolling means and rolling standard deviations are computed on shifted price series (in order to avoid data leakage from bar t to window t). Technical indicators such as Relative Strength Index (RSI), Moving Average Convergence Divergence (MACD) and exponential moving averages are added to the daily data ( Wang et al. 2021 ). The target is the next-step percentage return (defined as close[t + 1] − close[t]). After removing non-defined lag values or non-defined rolling statistics, we are left with 18 predictive lag features, which is the common feature space for all the models. Calendar features (day, month, hour, minute) and one-hot ticker information are added as side information. The features are scaled using statistics calculated over the training set to avoid leakage. For deep learning models (LSTM and QLSTM), the above matrix of 18 lagged features is reshaped into fixed-length windows of 15 timesteps. The state space for the reinforcement learning agent consists of the 18 lag features augmented with three portfolio variables (agent's current position, normalized cash balance, unrealized profit/loss). Table 1 summarizes the input features used in the framework. Table 1 Summary of input features used by the models. The same lag-based features are shared across classical, deep, reinforcement and quantum models. Feature Description Lagged close (t − 1 … t − 5) Past closing prices Lagged volume Past traded volume Lagged returns Past percentage returns Rolling mean / std From shifted series only RSI, MACD, EMA Daily-only technicals Position, cash, PnL RL agent state only 3.4 System Architecture The classical machine learning models — Decision Tree (max_depth = 10, min_samples_leaf = 20), Ridge regression (α = 1.0) and Gradient Boosting Regressor (500 estimators, learning rate = 0.02, max_depth = 5, subsample = 0.8) — are implemented using scikit-learn. The hyperparameters are selected so as to avoid commonly seen failure modes of unconstrained counterparts: a fully grown decision tree overfits by memorizing the train set; unregularized linear regression overfits by exploding under multicollinearity, yielding strongly negative test R². The Ridge penalty and the Gradient-Boosting subsample restore numerical stability without leakage. The deep learning models are implemented using TensorFlow/Keras and PyTorch ( Paszke et al. 2019 ). The ANN ( Grossi and Buscema 2008 ; Wen 2024 ) is a four-layer dense network (128–64–32–1) with ReLU activations, BatchNormalization, Dropout (0.3) and Adam optimizer. EarlyStopping with patience 10 is applied on a 10% inner validation split, drawn from the training set. The LSTM ( Moghar and Hamiche 2020 ; Staudemeyer and Morris 2019 ) is a two-layer stacked recurrent network of size (128–64) and a 15-step lookback window. It uses Backpropagation Through Time and applies Dropout (0.2) between layers and gradient clipping to prevent exploding gradients. The RL baseline agent is the Double Deep Q-Network ( Mnih et al. 2013 ). The state is the 21-dimension vector outlined earlier. The actions are: hold, buy, sell, short, cover in the daily context; hold, buy, sell in the intraday context ( Goluza et al. 2024 ). The reward is the clipped percentage portfolio value change in [− 1, 1] per time-step, plus a transaction cost of 1 bp per trade ( Sun et al. 2022 ). The Q-network is a 256–128–64 MLP, optimized with Smooth-L1 loss, an experience replay buffer of 200,000 transitions, target-network updates every three episodes, and an ε-greedy exploration policy where ε decays from 1.0 to 0.05 over 100 episodes. Gradient clipping at L2-norm 1.0 was used. The Q-models share a common variational quantum circuit (VQC) implemented with PennyLane ( Shapiro 2025 ) using its PyTorch wrapper. This VQC uses 4 qubits and 3 variational layers, encoding inputs via single-qubit RY rotations. Each layer applies trainable RY and RZ rotations on every qubit, followed by a circular CNOT entanglement structure. The Pauli-Z expectation is measured for every qubit, producing a 4-dimensional output vector of real numbers. With 4 qubits, 3 layers and 2 angles per qubit per layer, the quantum part yields 24 trainable parameters. The Quantum Neural Network (QNN) ( Beer 2022 ; Choudhary et al. 2025 ) is a feed-forward, hybrid architecture. Classical Linear(18 → 4) + tanh maps each lag feature vector to the 4-qubit input register. The VQC outputs a 4-vector, and then this is post-processed with a small classical MLP (Linear 4 → 16, ReLU, Linear 16 → 1). The QLSTM ( Chen et al. 2020 ; Kea et al. 2024 ) is a sequential network; each 15-step window of lag features is mapped to a 2-layer classical LSTM (hidden dimension 16), whose final hidden state is mapped through a learned Linear(16 → 4) projection (rather than the original code's hardcoded slice of the first 4 hidden states, which threw out 75% of the LSTM's state) to the qubit register. Then, this is followed by the same VQC and post-processing MLP ( Su and Li 2025 ). Finally, for the QDQN, the classical Double-DQN's Q-network's hidden layers are replaced with the VQC, as done in ( Dong et al. 2008 ; Jerbi et al. 2021 ) for parametrized quantum policies for RL. The 21-dimensional state is projected through Linear(21 → 4) + tanh and given to the VQC, whose 4 expectation values are fed to a final Linear(4 → 16, ReLU, 16 → 3) head outputting the Q-values. Two crucial implementation details were discovered to be necessary for trusting the quantum models. First, both the original QNN and QLSTM implement the per-sample quantum output with torch.tensor(q_out, dtype=torch.float32), silently detaching the quantum tensor from the PyTorch autograd graph. This zeroed out the gradients of the quantum parameters, so only the surrounding classical networks learned. This is fixed by stacking the per-sample outputs using torch.stack on the PennyLane-native tensor outputs, preserving the autograd path through the quantum circuit. One change alone is what distinguishes a hybrid network and a classical network with a frozen, random, quantum-themed head. Second is same-bar leakage at the feature level, which is mitigated by the lag pipeline described in Section 3.3 . All quantum runs are done on PennyLane's default.qubit simulator on CPU. Since each sample goes through the circuit individually, each forward pass takes approximately three orders of magnitude longer than the equivalent classical forward pass. In order to keep wall-clock time tractable, the quantum models are trained on a 5,000-sample chronologically-selected subset and evaluated on a 1,000-sample chronologically-selected subset. For paired comparisons against the classical networks, the same 1,000-sample test split is used. NumPy, PyTorch, TensorFlow, and Python's random module are all seeded with 42 for reproducibility. 3.5 Evaluation Protocol We assess two different but complementary perspectives of evaluation. Predictive performance measures are given by Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), test R² and directional accuracy, defined as the fraction of test samples for which the sign of the predicted return is the same as the sign of the realized return. We compare the performance to a constant zero predictor, which serves as our regression baseline. The MSE of the zero predictor in this case is nearly identical to the variance of the test targets, thus giving a lower bound on irreducible noise in the regression metric performance measures. Any model not exceeding this predictor will not deliver any actionable information. Trading performance measures are given by the cumulative return over the held-out test period, the Sharpe ratio, and the buy-and-hold portfolio as baseline strategy. The same held-out test set and the same transaction cost of 1 bp are applied to all trading strategies. The maximum drawdown of the strategy and the action profile (the percentage of bars on which the strategy takes a given action: long, short, flat etc.) are also reported, which inform on the strategy risk profile. 4 Results 4.1 Predictive Performance — One-Minute Intraday In Table 2 , the test-set metrics for the regression-style models on the one-minute intraday data are provided. None of the models perform better than a naive baseline (i.e., produce a positive test R²). The test error produced by the Ridge regressor, ANN and LSTM are each within about 1% of the naive test error MSE, and can be seen as essentially squandering the extra model capacity on noise. The Decision Tree and the Gradient Boosting perform much worse, showing their capacity is wasted on overfitting. The QLSTM is numerically within rounding error of the naive baseline and has the lowest MAE, but its predicted-vs-actual scatter plots are nearly flat and concentrated at zero (meaning it predicts essentially a constant conditional mean), and hence it also produces a negative R² value (see Fig. 2 ). The QNN converges in training loss, but test-set results show a consistently small negative offset, and hence a very large negative R² value (of about − 30) despite its small MAE, as shown in Fig. 1 . Table 2 Predictive metrics on the one-minute intraday data. Lower MSE and higher directional accuracy are better. “Beats BL” indicates whether the model’s MSE is strictly below the naive baseline. Model Test R² Test MSE Dir. Acc. Beats BL Decision Tree −0.923 5.32×10⁻⁵ 46.58% No Ridge Regression −0.005 2.78×10⁻⁵ 46.78% No Gradient Boosting −1.719 7.53×10⁻⁵ 46.14% No ANN −0.000 2.77×10⁻⁵ 46.78% No LSTM −0.007 2.79×10⁻⁵ 46.80% No QNN −29.99 1.36×10⁻⁵ 45.50% No QLSTM −0.012 4.46×10⁻⁷ 45.50% No Naive Baseline 0 2.77×10⁻⁵ 50.00% — 4.2 Predictive Performance — Daily Horizon The picture on daily data is a little better, although still very modest. The corresponding statistics are reported in Table 3 . The Ridge regressor has a test MSE slightly below the naive baseline; Decision Tree and Gradient Boosting are worse. All of the daily models' directional accuracy is around 50–52%, representing at most a very slim edge over chance. The QNN and QLSTM on daily data behave similarly to the classical ones, as is to be expected; the QLSTM training loss and predicted-vs-actual scatter on this horizon are shown in Fig. 4 . This agrees with the general conclusion that there exists a little more (still a very small) structure in daily data that the models can leverage on than one-minute data, which is more or less noise. Figure 3 compares the directional accuracy on the two time horizons. Table 3 Predictive metrics on the daily horizon. Model Test R² Test MSE Dir. Beats BL Decision Tree −0.060 8.91×10⁻⁴ 51.08% No Ridge −0.001 8.42×10⁻⁴ 50.76% Yes Gradient Boost. −0.003 8.43×10⁻⁴ 50.52% No ANN −0.0002 8.41×10⁻⁴ 51.23% ≈BL LSTM −0.001 8.42×10⁻⁴ 51.23% ≈BL QNN −0.024 9.37×10⁻⁴ 52.00% No QLSTM −0.313 1.13×10⁻³ 46.10% No Naive Baseline 0 8.43×10⁻⁴ 50.00% — 4.3 Trading Performance Table 4 shows the trading results for Double DQN, QDQN and buy-and-hold over the daily dataset, averaged across all eleven tickers. Double DQN performs with an average return of 13.04% and an average Sharpe ratio of 0.31, achieving significantly positive performance for AAPL (67.93%), AMZN (63.50%) and GOOGL (107.42%), while performing poorly for TSLA, META and SBUX; the episode reward, per-ticker portfolio trajectories and action distribution are shown in Fig. 5 . For the QDQN agent, despite using the same environment and reward function, a degenerate policy dominated by the buy action is learned. The average return achieved is a strongly negative − 33.29%. This is expected given the relatively limited capability of a 24-parameter quantum network acting as Q-network with 21-dimensional state space — the small quantum circuit is not providing the appropriate inductive bias to learn the correct policy. The corresponding intraday QDQN evaluation is shown in Fig. 6 . On the 1-minute intraday dataset, the QDQN along with the DQN achieve positive return relative to the buy-and-hold portfolio (− 63% loss), but negative in absolute terms (− 4.65% and − 6.45% respectively for the DQN and the QDQN). Table 4 Trading performance averaged across the eleven tickers on the daily horizon. The classical DQN produces a positive average return, whereas the QDQN learns a degenerate policy. Strategy Avg Return Avg Sharpe Beat B&H Double DQN + 13.04% 0.315 0/11 QDQN −33.29% −0.807 7/11 Buy-and-Hold varies — — 5 Discussion and Conclusion The most prominent takeaway from our experiments is that all of our well-regularized models — classical, deep, and quantum — all seem to converge to the same point in one-minute intraday data: the conditional mean of the next-step return given the lag features is nearly zero. The Ridge regressor, ANN, LSTM, and QLSTM are all within about 1% of the naive baseline's MSE. The unregularized tree and the over-parameterized Gradient Boosting model seem to fit training noise and degrade. This is the canonical behavior for data that looks like a random walk and is a property of the data, not of the architecture used. Both reinforcement learning and feature engineering proved more important than any sort of model exoticness on this task: the Double DQN agent, our only formulation that operates directly on the lag features, was the only configuration that reported a positive average return on the daily horizon, and it does so because its reward function is cumulative and it directly optimizes that reward function rather than the point-wise prediction error. The decision-making framing thus appears to be more natural for OHLCV data than the price-prediction framing. On the quantum side, after fixing the broken-gradient bug we found our QNN, QLSTM and QDQN trained as expected; however at far lower numbers of parameters (24 quantum angles plus a shallow classical wrapper) than our classical baselines, and the performance does not surpass their classical analogues on this data. We also see that our QNN at least trains to a degenerative fixed point on the intraday data: when the inherent signal-to-noise ratio is too low for any model to detect, the inductive bias of the model class is largely irrelevant. These results also serve as a cautionary note for quantum-finance papers which report very positive R² for intraday returns without stating how they account for same-bar leakage and gradient-flow detachment; our own pre-correction notebooks reported similarly optimistic numbers, and they were artefacts of these issues. There are a few obvious areas for improvement in the present study. The limits we placed on the quantum simulations — four qubits, three layers deep — are due to per-sample CPU simulation time, and so we believe there is a lot of scope for improvement in terms of expressivity by performing larger experiments either on dedicated hardware accelerators or on real NISQ devices; this is therefore left for future work ( Srivastava et al. 2023 ; Doosti et al. 2024 ). The trading agents were trained on subsampled data because of the same wall-clock constraint. The universe is composed of eleven diverse tickers, but it is still much smaller than a full equity universe. The evaluation consists of one chronological hold-out and, in order to further strengthen the conclusions, it would be worthwhile carrying out a multi-period rolling-window evaluation. Future directions to explore will include hybrid classical-quantum architectures with deeper circuits ( Qi et al. 2024 ; Bathala et al. 2025 ), improved data encoding schemes, and an evaluation across a wider range of market regimes. In summary, the outcome of this work is that variational quantum machine learning, as it is known today, is a promising yet not definitive tool to address stock market prediction; a careful experimental design — accurate lag features, normalization only on the training set, chronological splits ( Hasanov et al. 2022 ), gradient-flow correctness and realistic transaction costs — is no less relevant than the choice between a classical or a quantum algorithm. Declarations Competing Interests The authors have no relevant financial or non-financial interests to disclose. The authors have no competing interests to declare that are relevant to the content of this article. Ethics Approval Not applicable. This study does not involve human participants, human data or animal subjects. Clinical Trial Number Clinical trial number: not applicable. Consent to Participate Not applicable. Consent for Publication Not applicable. Funding The authors did not receive support from any organization for the submitted work. No funds, grants, or other support were received. Author Contribution P.S. conceived the study, designed the experimental framework and led the implementation of the quantum models (QNN, QLSTM and QDQN), including the gradient-flow correction in the PennyLane–PyTorch hybrid pipeline. P.S. and K.S. developed the leakage-free feature engineering pipeline and the chronological train/test splitting infrastructure used by all models. K.S. implemented the classical machine learning baselines (Decision Tree, Ridge regression and Gradient Boosting) and ran the corresponding experiments. T.V. implemented the deep learning models (ANN and LSTM) and produced the multi-timeframe comparison (1-minute, 5-minute and daily horizons). V.S. implemented the Double Deep Q-Network reinforcement learning agent, designed the trading environment, transaction-cost model and reward function, and produced the per-ticker trading evaluations. P.S., K.S., T.V. and V.S. jointly prepared all figures and tables. P.S. wrote the main manuscript text. V.J. supervised the work, reviewed the methodology, advised on the experimental design and interpretation of results, and provided critical revisions to the manuscript. All authors reviewed and approved the final manuscript. Data Availability The datasets analysed during the current study consist of historical OHLCV data for eleven large-cap U.S. equities — AAPL, AMZN, DIS, GOOGL, IBM, KO, META, MSFT, NVDA, SBUX and TSLA — at one-minute, five-minute and daily granularities. The raw data are publicly available from Yahoo Finance (https://finance.yahoo.com/) and were retrieved using the yfinance Python library. The processed datasets, the leakage-free feature engineering pipeline, the trained model artefacts and the analysis code that support the findings of this study are available from the corresponding author on reasonable request. References Antad S, Khandelwal S, Khandelwal A, Khandare R, Khandave P, Khangar D, Khanke R (2023) Stock price prediction website using linear regression — a machine learning algorithm. ITM Web of Conferences 56 Atesongun A, Gulsen M (2024) A hybrid forecasting structure based on ARIMA and artificial neural network models. Applied Sciences 14(16). https://www.mdpi.com/2076-3417/14/16/7122 Bathala SM, Leipold H, Adhikari B (2025) Contextual quantum neural networks for stock price prediction Beer K (2022) Quantum neural networks. arXiv preprint arXiv:2205.08154 Chaudhary R (2025) Advanced stock market prediction using long short-term memory networks: A comprehensive deep learning framework. https://arxiv.org/abs/2505.05325 Chen SY-C, Yoo S, Fang Y-LL (2020) Quantum long short-term memory. https://arxiv.org/abs/2009.01783 Chen T, Guestrin C (2016) XGBoost: A scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’16, ACM, pp 785–794. https://doi.org/10.1145/2939672.2939785 Choudhary PK, Innan N, Shafique M, Singh R (2025) HQNN-FSP: A hybrid classical-quantum neural network for regression-based financial stock market prediction. https://arxiv.org/abs/2503.15403 Cutler A, Cutler D, Stevens J (2011) Random forests. In: Ensemble Machine Learning, vol 45, pp 157–176 Dey R, Salem F (2017) Gate-variants of gated recurrent unit (GRU) neural networks Dong D, Chen C, Li H, Tarn T-J (2008) Quantum reinforcement learning. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 38(5):1207–1220. https://doi.org/10.1109/TSMCB.2008.925743 Doosti M, Wallden P, Hamill CB, Hankache R, Brown OT, Heunen C (2024) A brief review of quantum machine learning for financial services. https://arxiv.org/abs/2407.12618 Fabiha ST, Mumu RJ, Aktar F, Hossain BMM (2025) A regression-based share market prediction model for Bangladesh. https://arxiv.org/abs/2507.18643 Fattah J, Ezzine L, Aman Z, Moussami H, Lachhab A (2018) Forecasting of demand using ARIMA model. International Journal of Engineering Business Management 10:184797901880867 Ghasemi M, Ebrahimi D (2024) Introduction to reinforcement learning. https://arxiv.org/abs/2408.07712 Goluza S, Kovačević T, Bauman T, Kostanjčar Z (2024) Deep reinforcement learning with positional context for intraday trading. Evolving Systems 15(5):1865–1880. https://doi.org/10.1007/s12530-024-09593-6 Groenendijk J (2021) Predicting intraday stock returns using a hybrid ARIMA and long short-term memory neural network model. Master’s thesis, Erasmus School of Economics. http://hdl.handle.net/2105/60908 Grossi E, Buscema M (2008) Introduction to artificial neural networks. European Journal of Gastroenterology and Hepatology 19:1046–1054 Hasanov M, Wolter M, Glende E (2022) Time series data splitting for short-term load forecasting. In: PESS + PELSS 2022; Power and Energy Student Summit, pp 1–6 Ingle V, Deshmukh S (2021) Ensemble deep learning framework for stock market data prediction (EDLF-DP). Global Transitions Proceedings 2(1):47–66 Jadama A, Toray M (2024) Ensemble learning: Methods, techniques, application Javadi-Abhari A, Treinish M, Krsulich K, Wood CJ, Lishman J, Gacon J, Martiel S, Nation PD, Bishop LS, Cross AW, Johnson BR, Gambetta JM (2024) Quantum computing with Qiskit. https://arxiv.org/abs/2405.08810 Jerbi S, Gyurik C, Marshall SC, Briegel HJ, Dunjko V (2021) Parametrized quantum policies for reinforcement learning. https://arxiv.org/abs/2103.05577 Jijo B, Abdulazeez A (2021) Classification based on decision tree algorithm for machine learning. Journal of Applied Science and Technology Trends 2:20–28 Kang S (2025) Stock price prediction using triple barrier labeling and raw OHLCV data: Evidence from Korean markets Kea K, Kim D, Huot C, Kim T-K, Han Y (2024) A hybrid quantum-classical model for stock price prediction using quantum-enhanced long short-term memory. Entropy 26(11) Kumari K, Yadav S (2018) Linear regression analysis study. Journal of the Practice of Cardiovascular Sciences 4:33 Marisetty N (2024) Evaluating the efficacy of GARCH models in forecasting volatility dynamics across major global financial indices: A decade-long analysis. Journal of Economics Management and Trade 30:16–33 Mnih V, Kavukcuoglu K, Silver D, Graves A, Antonoglou I, Wierstra D, Riedmiller M (2013) Playing Atari with deep reinforcement learning. https://arxiv.org/abs/1312.5602 Moghar A, Hamiche M (2020) Stock market prediction using LSTM recurrent neural network. Procedia Computer Science 170:1168–1173 Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, Lin Z, Gimelshein N, Antiga L, Desmaison A, Köpf A, Yang E, DeVito Z, Raison M, Tejani A, Chilamkurthy S, Steiner B, Fang L, Bai J, Chintala S (2019) PyTorch: An imperative style, high-performance deep learning library. https://arxiv.org/abs/1912.01703 Pricope T-V (2021) Deep reinforcement learning in quantitative algorithmic trading: A review. https://arxiv.org/abs/2106.00123 Qi J, Yang C-H, Chen SY-C, Chen P-Y (2024) Quantum machine learning: An interplay between quantum computing and machine learning. https://arxiv.org/abs/2411.09403 Ravina, Shrivastav A (2025) Short-term stock price prediction using ANN and LSTM: A comparative study on Indian tech companies. Grenze International Journal of Engineering and Technology 11(2):295–308 Rokach L, Maimon O (2005) Decision trees. In: Data Mining and Knowledge Discovery Handbook, vol 6, pp 165–192 Salman H, Kalakech A, Steiti A (2024) Random forest algorithm overview. Babylonian Journal of Machine Learning 2024:69–79 Shapiro S (2025) Hybrid quantum-classical machine learning with PennyLane: A comprehensive guide for computational research Srivastava N, Belekar G, Shahakar N, Babu AH (2023) The potential of quantum techniques for stock price prediction. In: 2023 IEEE International Conference on Recent Advances in Systems Science and Engineering (RASSE), pp 1–7 Staudemeyer RC, Morris ER (2019) Understanding LSTM — a tutorial into long short-term memory recurrent neural networks. https://arxiv.org/abs/1909.09586 Su L, Li D (2025) BLS-QLSTM: A novel hybrid quantum neural network for stock index forecasting. Humanities and Social Sciences Communications Sun S, Xue W, Wang R, He X, Zhu J, Li J, An B (2022) DeepScalper: A risk-aware reinforcement learning framework to capture fleeting intraday trading opportunities. https://arxiv.org/abs/2201.09058 Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN, Kaiser L, Polosukhin I (2017) Attention is all you need. https://arxiv.org/pdf/1706.03762.pdf Wang Q, Zhou Y, Shen J (2021) Intraday trading strategy based on time series and machine learning for Chinese stock market. https://arxiv.org/abs/2103.13507 Wen H (2024) Prediction of stock price by neural network based on CNN, LSTM, ANN. Advances in Economics, Management and Political Sciences 87:229–237 Wu Y (2023) Stock price prediction based on simple decision tree, random forest and XGBoost. BCP Business Management 38:3383–3388 Xiao J, Deng T, Bi S (2024) Comparative analysis of LSTM, GRU, and transformer models for stock price prediction. https://arxiv.org/abs/2411.05790 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9653068","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":638840408,"identity":"c0de6815-78c0-4734-aaa7-e8271e84f5f1","order_by":0,"name":"Pratham Shah","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBElEQVRIiWNgGAWjYHACNgbGBoYEfvbmAyAeMxCCgARhLZI9xxLAWniI1mJwI8cAzOUh5Cpz6fZnD37uYMhjOJDz8cMHhsPs9uwMjB9+MFjk4dJiOeeMuWHvGYZixoazmyVnMBwGOYxZsodBohiXFqB72CR42xgSmxl7tzHzMKSB/SIN9EtiA04t6c8k/wK1tDHzPGP+A9HC/Bu/lgQzaZAtPWw8bEDzbUBa2PDbcueMmbRsG0OxBA+bsWSPAVDLYcY2yx4DPFputz+TfNvGkGd///HDDz8qJJLZ+w8fvvGjog6nFmiU/YeZwJDMAIomBgNc6hkwY9kOj9pRMApGwSgYoQAATKVLMSgKGtkAAAAASUVORK5CYII=","orcid":"","institution":"Veermata Jijabai Technological Institute","correspondingAuthor":true,"prefix":"","firstName":"Pratham","middleName":"","lastName":"Shah","suffix":""},{"id":638840409,"identity":"e5274e41-87fe-497b-bffe-aad3f38e7e96","order_by":1,"name":"Kshitij Shah","email":"","orcid":"","institution":"Veermata Jijabai Technological Institute","correspondingAuthor":false,"prefix":"","firstName":"Kshitij","middleName":"","lastName":"Shah","suffix":""},{"id":638840410,"identity":"910adac9-1dc1-4308-8f0b-442093b44a89","order_by":2,"name":"Tvisha Vedant","email":"","orcid":"","institution":"Veermata Jijabai Technological Institute","correspondingAuthor":false,"prefix":"","firstName":"Tvisha","middleName":"","lastName":"Vedant","suffix":""},{"id":638840411,"identity":"4d710760-bc29-4052-93a8-40cbd78006c3","order_by":3,"name":"Vatsal Shah","email":"","orcid":"","institution":"Veermata Jijabai Technological Institute","correspondingAuthor":false,"prefix":"","firstName":"Vatsal","middleName":"","lastName":"Shah","suffix":""},{"id":638840412,"identity":"5c1cd123-ac64-40d9-ae81-94863d836133","order_by":4,"name":"Varshapriya Jyotinagar","email":"","orcid":"","institution":"Veermata Jijabai Technological Institute","correspondingAuthor":false,"prefix":"","firstName":"Varshapriya","middleName":"","lastName":"Jyotinagar","suffix":""}],"badges":[],"createdAt":"2026-05-08 10:53:40","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9653068/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9653068/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109248143,"identity":"ad6838e7-4ba6-470d-9a2d-0399667e74e4","added_by":"auto","created_at":"2026-05-14 08:29:00","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":104474,"visible":true,"origin":"","legend":"\u003cp\u003eQNN intraday evaluation: training loss, prediction trace, predicted-vs-actual scatter and residual histogram. The scatter shows the degenerate near-constant fixed point.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-9653068/v1/f54c1db53d98b02ee9b90d2a.png"},{"id":109252461,"identity":"109bf4e7-c5e7-467e-a2cd-f4486b02fed2","added_by":"auto","created_at":"2026-05-14 09:26:48","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":95208,"visible":true,"origin":"","legend":"\u003cp\u003eQLSTM intraday evaluation. The scatter collapses to a near-horizontal line at zero, indicating that the model is predicting the unconditional mean of the next-step return.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-9653068/v1/6b929dddf843ab831939a8c1.png"},{"id":109248148,"identity":"2e9e9c89-914e-4087-8db1-f895dcf0e7f8","added_by":"auto","created_at":"2026-05-14 08:29:01","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":40884,"visible":true,"origin":"","legend":"\u003cp\u003eOne-minute intraday vs daily horizon: test R² and directional accuracy for Ridge, Gradient Boosting, ANN and LSTM. The directional accuracy on the daily horizon is consistently above 50%, whereas the intraday models cluster around 46–47%.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-9653068/v1/77ab790c3da78c2a74764bf6.png"},{"id":109249519,"identity":"af219fba-e6eb-4bf7-915e-a369b25314d3","added_by":"auto","created_at":"2026-05-14 08:55:07","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":129481,"visible":true,"origin":"","legend":"\u003cp\u003eClassical Double DQN trading evaluation on daily data: episode reward, per-ticker portfolio trajectories and action distribution.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-9653068/v1/3c35501076448c9502a889a2.png"},{"id":109249680,"identity":"763da698-6966-4b6b-b72b-e55777801db1","added_by":"auto","created_at":"2026-05-14 08:58:55","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":101086,"visible":true,"origin":"","legend":"\u003cp\u003eQDQN trading evaluation on intraday data. The portfolio trajectory is qualitatively similar to the classical DQN but the agent is more trade-hungry and finishes lower.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-9653068/v1/28fd864ec606249ec8cf7777.png"},{"id":109252394,"identity":"9ae53335-b04e-4f6f-86d2-4ebb8fef7fe3","added_by":"auto","created_at":"2026-05-14 09:25:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":614872,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9653068/v1/f1cd6d64-e2fc-4ffc-910f-c10db9e2a2fb.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Stock Prediction and Trading from OHLCV Data: A Quantum- Enhanced Learning-Based Comparison","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eThe financial markets play a vital role in today's economy and their roles include investment, capital allocation, and risk management. Hence, stock price forecasting is of immense importance for academics, traders, and many other financial institutions. An accurate forecast, even by a very little difference, will help to make optimal allocation of portfolio, intelligent trading and other financial decisions. Despite that, stock market forecasting is of very challenging nature because of the characteristics of the financial data.\u003c/p\u003e \u003cp\u003eThe characteristics of financial time series are different from majority of structured datasets used in machine learning applications. They exhibit strong volatility, non-stationarity and very noisy behaviour (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eKang 2025\u003c/span\u003e). Market trends are influenced by many macro-economic, geopolitical and various unpredictable factors. They influence time series in a nonlinear manner. Most early research regarding financial forecasting was done using classical statistical methods such as ARIMA and GARCH (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eFattah et al. 2018\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMarisetty 2024\u003c/span\u003e) and these models inherently assume stationarity and linear relationships of the underlying time series. They are interpretable and have a theoretical foundation, but do not perform well for complex nonlinear relationships (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAtesongun and Gulsen 2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThanks to the growth of computing power and large amounts of historical data, the topic has shifted towards machine learning (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eWang et al. 2021\u003c/span\u003e). In the recent time, deep learning models such as Recurrent Neural Networks and Long Short-Term Memory (LSTM) (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMoghar and Hamiche 2020\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eStaudemeyer and Morris 2019\u003c/span\u003e) have yielded very promising results on sequence-based prediction tasks. At the same time, reinforcement learning (RL) has also been proposed as a trading framework (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ePricope 2021\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGhasemi and Ebrahimi 2024\u003c/span\u003e). Unlike supervised methods where the task is to predict price, RL can be defined as a sequence of decision-making tasks aiming at maximizing the long-term reward. The appearance of NISQ hardware has also expanded the prospect of QML for financial prediction (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSrivastava et al. 2023\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDoosti et al. 2024\u003c/span\u003e); VQCs can be interpreted as differentiable layers within classical neural networks (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eBeer 2022\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eQi et al. 2024\u003c/span\u003e), and these have been proposed to offer an inductive bias that cannot be simulated with classical methods.\u003c/p\u003e \u003cp\u003eDespite the abundance of research conducted on each of the methods above, few direct comparative studies between the four learning paradigms are conducted on a level playing field. Studies in the existing literature vary in dataset, feature preprocessing pipeline and metric used. This paper aims to fill in that void by introducing a standardized methodology for training and evaluating traditional machine learning models, deep learning models, deep reinforcement learning agents and their quantum-enhanced counterparts. Training and testing is performed on the same dataset, using the same leakage-free feature pipeline and the same time-chronological train/test split. Emphasis is placed on the quantum family of models \u0026mdash; QNN, QLSTM, and QDQN \u0026mdash; and on identifying when they might outperform their classical counterparts and when they do not, across different time frames (1-minute, 5-minute and daily). Key contributions of this paper are: (i) an equal empirical study of nine distinct models spanning all four learning paradigms on the same data; (ii) a rigorous methodology write-up detailing the essential adjustments that must be made to yield reliable results, most notably a gradient-flow correction applied to the hybrid PennyLane\u0026ndash;PyTorch models; and (iii) a study of the models across various time horizons to reveal dependence of model superiority on data horizons.\u003c/p\u003e"},{"header":"2 Technical Overview","content":"\u003cp\u003eStock market prediction has been studied extensively in many sub-fields of statistics, machine learning, deep learning, reinforcement learning and, more recently, quantum machine learning. Over the years the research has progressed from simple statistical methods towards more complex data-driven and learning-based approaches. The early studies were based on statistical methods such as ARIMA and GARCH (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eFattah et al. 2018\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMarisetty 2024\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGroenendijk 2021\u003c/span\u003e). These methods are designed to capture temporal dependencies in the data and they work reasonably well on relatively stable and stationary series. They are also interpretable, which is desirable for financial decision-making. However, the assumptions on which these methods are built are rarely satisfied in real markets, where the underlying regime can change, volatility can shift abruptly and external economic events can introduce sharp non-linearities (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAtesongun and Gulsen 2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAfter the emergence of higher computational resources, classical machine learning algorithms such as Linear Regression, Decision Tree and Random Forest were applied to the stock prediction problem (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAntad et al. 2023\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eKumari and Yadav 2018\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eFabiha et al. 2025\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eJijo and Abdulazeez 2021\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eRokach and Maimon 2005\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eWu 2023\u003c/span\u003e). Among these, the Random Forest algorithm received considerable attention because of its ability to reduce variance through ensembling (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCutler et al. 2011\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eJadama and Toray 2024\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSalman et al. 2024\u003c/span\u003e). Gradient boosted tree methods such as XGBoost have also been shown to be competitive on related tasks (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eChen and Guestrin 2016\u003c/span\u003e). However, classical machine learning models cannot easily model the long-range temporal dependencies in the data, and their performance is highly dependent on the quality of the engineered features. Artificial Neural Networks (ANNs) and Long Short-Term Memory (LSTM) networks helped to overcome some of these limitations. ANN-based feed-forward models were among the first deep learning techniques used for financial forecasting and they have been shown to capture nonlinear patterns better than classical models (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGrossi and Buscema 2008\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eWen 2024\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eIngle and Deshmukh 2021\u003c/span\u003e). LSTMs went a step further and provided an explicit mechanism for retaining memory, which makes them suitable for stock price prediction (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMoghar and Hamiche 2020\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eChaudhary 2025\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eRavina and Shrivastav 2025\u003c/span\u003e). Other recurrent variants such as the GRU (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDey and Salem 2017\u003c/span\u003e) and attention-based models such as the Transformer (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eVaswani et al. 2017\u003c/span\u003e) have also been compared on similar problems (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eXiao et al. 2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eSimultaneously to research in predictive modeling, the concept of using reinforcement learning (RL) in financial trading has been explored as another alternative paradigm (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ePricope 2021\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGhasemi and Ebrahimi 2024\u003c/span\u003e). An RL setup represents financial trading as a sequence of decision-making actions performed by an agent within a market environment, with the possible actions being to buy, sell or hold, and a reward associated with the resulting portfolio value change. The Deep Q-Network (DQN) algorithm (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMnih et al. 2013\u003c/span\u003e) has been proposed in the context of such tasks by enabling approximate learning of the value function in high-dimensional situations using deep neural networks. More recent extensions have looked into risk-sensitive rewards (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSun et al. 2022\u003c/span\u003e), more complex state representations (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGoluza et al. 2024\u003c/span\u003e), or the explicit modelling of transaction costs.\u003c/p\u003e \u003cp\u003eA much newer paradigm has emerged as quantum machine learning (QML) (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSrivastava et al. 2023\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDoosti et al. 2024\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eQi et al. 2024\u003c/span\u003e). The general structure used to date for QML-based financial prediction is to wrap a small, parametrised quantum circuit into a classical neural network and train the hybrid network end-to-end. Specifically Quantum Neural Networks (QNN) (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eBeer 2022\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eChoudhary et al. 2025\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eBathala et al. 2025\u003c/span\u003e), Quantum LSTMs (QLSTM) (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eChen et al. 2020\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eKea et al. 2024\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSu and Li 2025\u003c/span\u003e) and Quantum Reinforcement Learning agents (QRL/QDQN) (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDong et al. 2008\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eJerbi et al. 2021\u003c/span\u003e) have been proposed in the literature as quantum equivalents to the already existing ML, DL and RL models. It is believed that using a quantum circuit may increase the richness of feature representations through superposition and entanglement. However, the practical use of these methods raises issues. First, gradient signals can silently get \u0026ldquo;broken\u0026rdquo; at the quantum component, i.e., lost, when there is an issue with the framework's plumbing code. In this case apparent training of the quantum model happens while, in fact, only a classical model with frozen random projection is trained. Second, simulation of the quantum computation cost can grow very quickly with number of qubits and circuit depth; this limits the sizes of the problem that can be explored. However, applying frameworks such as Qiskit (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eJavadi-Abhari et al. 2024\u003c/span\u003e) or PennyLane (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eShapiro 2025\u003c/span\u003e) allows applied researchers to perform experiments of this kind increasingly easily.\u003c/p\u003e \u003cp\u003eAn aspect that is pointed out repeatedly in all the reviews of the area is the lack of a single best model; the outcome depends on a number of factors, among them quality of data, feature engineering and market regime. Several pitfalls are also identified in the literature: models are prone to overfitting, i.e., their performance on training data fails to generalize; there is often no agreement on the methodology of experimental tests, thus hindering comparisons between studies; most predictive models are not adapted into a trading strategy; few RL approaches include comparisons with predictive models. Models for the different paradigms are generally analyzed separately, if at all. The motivation of this paper is the lack of unity pointed out in those papers; the goal is to present a comprehensive comparison of all the four paradigms, ML, DL, RL and QML within a unified framework.\u003c/p\u003e"},{"header":"3 Methodology","content":"\u003cp\u003eIn view of the lacunae indicated above, the methodology of the work carried out in this paper is designed in a principled and experimental manner so that impartial and reproducible comparisons between the four learning paradigms are possible. Whereas the vast majority of the published research concerning stock prediction and trading utilizes independent models and varying experimental settings, the work herein is aimed at utilizing the same datasets with the same chronological train/test split for all the four model categories. Since financial time series data are non-stationary, noisy and often incorporate complex non-linear relationships, the methodology goes beyond pure predictive accuracy and instead also compares the models in a simulated trading environment. Significant focus is dedicated to the quantum-domain models \u0026mdash; QNN, QLSTM and QDQN \u0026mdash; as well as on the practical difficulties encountered during the implementation of such models. The well-established classical machine learning, deep learning and reinforcement learning based methods are maintained as benchmarks and principled baselines to establish any purported advantages from quantum approaches against established concepts. This methodology consists of five main stages: design of the research, data specification, pre-processing and feature engineering, implementation across several time-scales (1 minute, 5 minute and daily), and evaluation. Each stage is detailed in the ensuing subsections.\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Research Design\u003c/h2\u003e \u003cp\u003eThe research design followed in this work is experiment-driven and focuses on enabling fair comparisons between the four learning paradigms investigated. All models are trained and tested over the same dataset and on the same 80/20 chronological split. The same set of lagged features is used wherever possible as input, the same metrics are used for evaluation, and significant care has been taken to eliminate potential forms of data leakage. The workflow consists of five stages: data description, data preprocessing and feature engineering, model implementation across timeframes, evaluation protocol, and analysis of the results. For describing implementation details, emphasis has been placed on quantum-domain models in line with the main direction of this research.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Data Description\u003c/h2\u003e \u003cp\u003eThe historical stock data used throughout this work are presented in the conventional OHLCV (Open\u0026ndash;High\u0026ndash;Low\u0026ndash;Close\u0026ndash;Volume) format (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eKang 2025\u003c/span\u003e), standard in quantitative finance. Each record represents the overall movement of price over a period, accompanied by the traded volume. The data used comprise eleven large-cap U.S. equities \u0026mdash; AAPL, AMZN, DIS, GOOGL, IBM, KO, META, MSFT, NVDA, SBUX and TSLA. Two different levels of granularities of the same dataset have been explored. The intraday dataset consists of 209,498 one-minute bars (a 5-minute aggregated version has been further examined), whereas the daily dataset contains about 27,500 daily bars corresponding to the same tickers. The selection of liquid large-cap equities minimizes the influence of possible illiquid events. The intraday data serves as a useful evaluation ground on a low signal-to-noise data problem, whereas the daily data contains smoother trends and is closer to the regime where other research has performed analyses (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eWang et al. 2021\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eChaudhary 2025\u003c/span\u003e). The dataset spans across different market phases, i.e., bullish, bearish and sideway states, and this ensures that the comparison is relevant. The chronological 80/20 split (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eHasanov et al. 2022\u003c/span\u003e) ensures that time ordering is maintained.\u003c/p\u003e \u003cp\u003eThere are a number of known statistical properties of financial time series that guide the modelling. They are non-stationary (moments vary over time), and exhibit volatility clustering (high volatility episodes tend to follow high volatility). Return distributions are fat-tailed (extreme events are more probable than under a normal distribution). These properties motivate both non-linear sequential models and the use of reinforcement learning where the states can be adjusted via continuous interaction with the environment.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Data Preprocessing and Feature Engineering\u003c/h2\u003e \u003cp\u003eThe preprocessing is carried out chronologically to maintain the time-series structure. Missing values are filled with interpolated values according to gap patterns. Outliers (mostly caused by anomalous trading events) are clipped to statistically computed moving bounds. Feature engineering \u0026mdash; the most crucial part of the pipeline \u0026mdash; is designed to avoid same-bar leakage, which is an important pitfall when predicting based on OHLCV data. If close or return on bar t is predicted using OHLCV on the same bar t, then the low and high, by construction, enclose the close. This would result in artificially high R\u0026sup2; values, and an inaccurate model for future trading. This is avoided by only using lagged data.\u003c/p\u003e \u003cp\u003eAt time t we compute five lagged values (t\u0026thinsp;\u0026minus;\u0026thinsp;1 to t\u0026thinsp;\u0026minus;\u0026thinsp;5) of close, volume, and simple percentage return. Rolling means and rolling standard deviations are computed on shifted price series (in order to avoid data leakage from bar t to window t). Technical indicators such as Relative Strength Index (RSI), Moving Average Convergence Divergence (MACD) and exponential moving averages are added to the daily data (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eWang et al. 2021\u003c/span\u003e). The target is the next-step percentage return (defined as close[t\u0026thinsp;+\u0026thinsp;1] \u0026minus; close[t]). After removing non-defined lag values or non-defined rolling statistics, we are left with 18 predictive lag features, which is the common feature space for all the models. Calendar features (day, month, hour, minute) and one-hot ticker information are added as side information. The features are scaled using statistics calculated over the training set to avoid leakage.\u003c/p\u003e \u003cp\u003eFor deep learning models (LSTM and QLSTM), the above matrix of 18 lagged features is reshaped into fixed-length windows of 15 timesteps. The state space for the reinforcement learning agent consists of the 18 lag features augmented with three portfolio variables (agent's current position, normalized cash balance, unrealized profit/loss). Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e summarizes the input features used in the framework.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of input features used by the models. The same lag-based features are shared across classical, deep, reinforcement and quantum models.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFeature\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLagged close (t\u0026thinsp;\u0026minus;\u0026thinsp;1 \u0026hellip; t\u0026thinsp;\u0026minus;\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePast closing prices\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLagged volume\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePast traded volume\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLagged returns\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePast percentage returns\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRolling mean / std\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFrom shifted series only\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRSI, MACD, EMA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDaily-only technicals\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePosition, cash, PnL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRL agent state only\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.4 System Architecture\u003c/h2\u003e \u003cp\u003eThe classical machine learning models \u0026mdash; Decision Tree (max_depth\u0026thinsp;=\u0026thinsp;10, min_samples_leaf\u0026thinsp;=\u0026thinsp;20), Ridge regression (α\u0026thinsp;=\u0026thinsp;1.0) and Gradient Boosting Regressor (500 estimators, learning rate\u0026thinsp;=\u0026thinsp;0.02, max_depth\u0026thinsp;=\u0026thinsp;5, subsample\u0026thinsp;=\u0026thinsp;0.8) \u0026mdash; are implemented using scikit-learn. The hyperparameters are selected so as to avoid commonly seen failure modes of unconstrained counterparts: a fully grown decision tree overfits by memorizing the train set; unregularized linear regression overfits by exploding under multicollinearity, yielding strongly negative test R\u0026sup2;. The Ridge penalty and the Gradient-Boosting subsample restore numerical stability without leakage.\u003c/p\u003e \u003cp\u003eThe deep learning models are implemented using TensorFlow/Keras and PyTorch (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ePaszke et al. 2019\u003c/span\u003e). The ANN (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGrossi and Buscema 2008\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eWen 2024\u003c/span\u003e) is a four-layer dense network (128\u0026ndash;64\u0026ndash;32\u0026ndash;1) with ReLU activations, BatchNormalization, Dropout (0.3) and Adam optimizer. EarlyStopping with patience 10 is applied on a 10% inner validation split, drawn from the training set. The LSTM (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMoghar and Hamiche 2020\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eStaudemeyer and Morris 2019\u003c/span\u003e) is a two-layer stacked recurrent network of size (128\u0026ndash;64) and a 15-step lookback window. It uses Backpropagation Through Time and applies Dropout (0.2) between layers and gradient clipping to prevent exploding gradients.\u003c/p\u003e \u003cp\u003eThe RL baseline agent is the Double Deep Q-Network (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMnih et al. 2013\u003c/span\u003e). The state is the 21-dimension vector outlined earlier. The actions are: hold, buy, sell, short, cover in the daily context; hold, buy, sell in the intraday context (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGoluza et al. 2024\u003c/span\u003e). The reward is the clipped percentage portfolio value change in [\u0026minus;\u0026thinsp;1, 1] per time-step, plus a transaction cost of 1 bp per trade (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSun et al. 2022\u003c/span\u003e). The Q-network is a 256\u0026ndash;128\u0026ndash;64 MLP, optimized with Smooth-L1 loss, an experience replay buffer of 200,000 transitions, target-network updates every three episodes, and an ε-greedy exploration policy where ε decays from 1.0 to 0.05 over 100 episodes. Gradient clipping at L2-norm 1.0 was used.\u003c/p\u003e \u003cp\u003eThe Q-models share a common variational quantum circuit (VQC) implemented with PennyLane (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eShapiro 2025\u003c/span\u003e) using its PyTorch wrapper. This VQC uses 4 qubits and 3 variational layers, encoding inputs via single-qubit RY rotations. Each layer applies trainable RY and RZ rotations on every qubit, followed by a circular CNOT entanglement structure. The Pauli-Z expectation is measured for every qubit, producing a 4-dimensional output vector of real numbers. With 4 qubits, 3 layers and 2 angles per qubit per layer, the quantum part yields 24 trainable parameters.\u003c/p\u003e \u003cp\u003eThe Quantum Neural Network (QNN) (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eBeer 2022\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eChoudhary et al. 2025\u003c/span\u003e) is a feed-forward, hybrid architecture. Classical Linear(18 \u0026rarr; 4) + tanh maps each lag feature vector to the 4-qubit input register. The VQC outputs a 4-vector, and then this is post-processed with a small classical MLP (Linear 4 \u0026rarr; 16, ReLU, Linear 16 \u0026rarr; 1). The QLSTM (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eChen et al. 2020\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eKea et al. 2024\u003c/span\u003e) is a sequential network; each 15-step window of lag features is mapped to a 2-layer classical LSTM (hidden dimension 16), whose final hidden state is mapped through a learned Linear(16 \u0026rarr; 4) projection (rather than the original code's hardcoded slice of the first 4 hidden states, which threw out 75% of the LSTM's state) to the qubit register. Then, this is followed by the same VQC and post-processing MLP (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSu and Li 2025\u003c/span\u003e). Finally, for the QDQN, the classical Double-DQN's Q-network's hidden layers are replaced with the VQC, as done in (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDong et al. 2008\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eJerbi et al. 2021\u003c/span\u003e) for parametrized quantum policies for RL. The 21-dimensional state is projected through Linear(21 \u0026rarr; 4) + tanh and given to the VQC, whose 4 expectation values are fed to a final Linear(4 \u0026rarr; 16, ReLU, 16 \u0026rarr; 3) head outputting the Q-values.\u003c/p\u003e \u003cp\u003eTwo crucial implementation details were discovered to be necessary for trusting the quantum models. First, both the original QNN and QLSTM implement the per-sample quantum output with torch.tensor(q_out, dtype=torch.float32), silently detaching the quantum tensor from the PyTorch autograd graph. This zeroed out the gradients of the quantum parameters, so only the surrounding classical networks learned. This is fixed by stacking the per-sample outputs using torch.stack on the PennyLane-native tensor outputs, preserving the autograd path through the quantum circuit. One change alone is what distinguishes a hybrid network and a classical network with a frozen, random, quantum-themed head. Second is same-bar leakage at the feature level, which is mitigated by the lag pipeline described in Section \u003cspan refid=\"Sec6\" class=\"InternalRef\"\u003e3.3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eAll quantum runs are done on PennyLane's default.qubit simulator on CPU. Since each sample goes through the circuit individually, each forward pass takes approximately three orders of magnitude longer than the equivalent classical forward pass. In order to keep wall-clock time tractable, the quantum models are trained on a 5,000-sample chronologically-selected subset and evaluated on a 1,000-sample chronologically-selected subset. For paired comparisons against the classical networks, the same 1,000-sample test split is used. NumPy, PyTorch, TensorFlow, and Python's random module are all seeded with 42 for reproducibility.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Evaluation Protocol\u003c/h2\u003e \u003cp\u003eWe assess two different but complementary perspectives of evaluation. Predictive performance measures are given by Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), test R\u0026sup2; and directional accuracy, defined as the fraction of test samples for which the sign of the predicted return is the same as the sign of the realized return. We compare the performance to a constant zero predictor, which serves as our regression baseline. The MSE of the zero predictor in this case is nearly identical to the variance of the test targets, thus giving a lower bound on irreducible noise in the regression metric performance measures. Any model not exceeding this predictor will not deliver any actionable information.\u003c/p\u003e \u003cp\u003eTrading performance measures are given by the cumulative return over the held-out test period, the Sharpe ratio, and the buy-and-hold portfolio as baseline strategy. The same held-out test set and the same transaction cost of 1 bp are applied to all trading strategies. The maximum drawdown of the strategy and the action profile (the percentage of bars on which the strategy takes a given action: long, short, flat etc.) are also reported, which inform on the strategy risk profile.\u003c/p\u003e \u003c/div\u003e"},{"header":"4 Results","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Predictive Performance \u0026mdash; One-Minute Intraday\u003c/h2\u003e \u003cp\u003eIn Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the test-set metrics for the regression-style models on the one-minute intraday data are provided. None of the models perform better than a naive baseline (i.e., produce a positive test R\u0026sup2;). The test error produced by the Ridge regressor, ANN and LSTM are each within about 1% of the naive test error MSE, and can be seen as essentially squandering the extra model capacity on noise. The Decision Tree and the Gradient Boosting perform much worse, showing their capacity is wasted on overfitting. The QLSTM is numerically within rounding error of the naive baseline and has the lowest MAE, but its predicted-vs-actual scatter plots are nearly flat and concentrated at zero (meaning it predicts essentially a constant conditional mean), and hence it also produces a negative R\u0026sup2; value (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The QNN converges in training loss, but test-set results show a consistently small negative offset, and hence a very large negative R\u0026sup2; value (of about\u0026thinsp;\u0026minus;\u0026thinsp;30) despite its small MAE, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePredictive metrics on the one-minute intraday data. Lower MSE and higher directional accuracy are better. \u0026ldquo;Beats BL\u0026rdquo; indicates whether the model\u0026rsquo;s MSE is strictly below the naive baseline.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026times;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTest R\u0026sup2;\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTest MSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDir. Acc.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBeats BL\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDecision Tree\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.923\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e5.32\u0026times;10⁻⁵\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.58%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRidge Regression\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e2.78\u0026times;10⁻⁵\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.78%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGradient Boosting\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;1.719\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e7.53\u0026times;10⁻⁵\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.14%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eANN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e2.77\u0026times;10⁻⁵\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.78%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e2.79\u0026times;10⁻⁵\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.80%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eQNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;29.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e1.36\u0026times;10⁻⁵\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e45.50%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eQLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e4.46\u0026times;10⁻⁷\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e45.50%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eNaive Baseline\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e2.77\u0026times;10⁻⁵\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e50.00%\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e\u0026mdash;\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Predictive Performance \u0026mdash; Daily Horizon\u003c/h2\u003e \u003cp\u003eThe picture on daily data is a little better, although still very modest. The corresponding statistics are reported in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The Ridge regressor has a test MSE slightly below the naive baseline; Decision Tree and Gradient Boosting are worse. All of the daily models' directional accuracy is around 50\u0026ndash;52%, representing at most a very slim edge over chance. The QNN and QLSTM on daily data behave similarly to the classical ones, as is to be expected; the QLSTM training loss and predicted-vs-actual scatter on this horizon are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. This agrees with the general conclusion that there exists a little more (still a very small) structure in daily data that the models can leverage on than one-minute data, which is more or less noise. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e compares the directional accuracy on the two time horizons.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePredictive metrics on the daily horizon.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026times;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTest R\u0026sup2;\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTest MSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDir.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBeats BL\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDecision Tree\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e8.91\u0026times;10⁻⁴\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e51.08%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRidge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e8.42\u0026times;10⁻⁴\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e50.76%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGradient Boost.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e8.43\u0026times;10⁻⁴\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e50.52%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eANN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.0002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e8.41\u0026times;10⁻⁴\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e51.23%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026asymp;BL\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e8.42\u0026times;10⁻⁴\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e51.23%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026asymp;BL\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eQNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e9.37\u0026times;10⁻⁴\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e52.00%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eQLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.313\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e1.13\u0026times;10⁻\u0026sup3;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.10%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eNaive Baseline\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e8.43\u0026times;10⁻⁴\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e50.00%\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e\u0026mdash;\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Trading Performance\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the trading results for Double DQN, QDQN and buy-and-hold over the daily dataset, averaged across all eleven tickers. Double DQN performs with an average return of 13.04% and an average Sharpe ratio of 0.31, achieving significantly positive performance for AAPL (67.93%), AMZN (63.50%) and GOOGL (107.42%), while performing poorly for TSLA, META and SBUX; the episode reward, per-ticker portfolio trajectories and action distribution are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. For the QDQN agent, despite using the same environment and reward function, a degenerate policy dominated by the buy action is learned. The average return achieved is a strongly negative\u0026thinsp;\u0026minus;\u0026thinsp;33.29%. This is expected given the relatively limited capability of a 24-parameter quantum network acting as Q-network with 21-dimensional state space \u0026mdash; the small quantum circuit is not providing the appropriate inductive bias to learn the correct policy. The corresponding intraday QDQN evaluation is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. On the 1-minute intraday dataset, the QDQN along with the DQN achieve positive return relative to the buy-and-hold portfolio (\u0026minus;\u0026thinsp;63% loss), but negative in absolute terms (\u0026minus;\u0026thinsp;4.65% and \u0026minus;\u0026thinsp;6.45% respectively for the DQN and the QDQN).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTrading performance averaged across the eleven tickers on the daily horizon. The classical DQN produces a positive average return, whereas the QDQN learns a degenerate policy.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStrategy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAvg Return\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAvg Sharpe\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBeat B\u0026amp;H\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDouble DQN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e+\u0026thinsp;13.04%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.315\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0/11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eQDQN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;33.29%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.807\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7/11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBuy-and-Hold\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003evaries\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5 Discussion and Conclusion","content":"\u003cp\u003eThe most prominent takeaway from our experiments is that all of our well-regularized models \u0026mdash; classical, deep, and quantum \u0026mdash; all seem to converge to the same point in one-minute intraday data: the conditional mean of the next-step return given the lag features is nearly zero. The Ridge regressor, ANN, LSTM, and QLSTM are all within about 1% of the naive baseline's MSE. The unregularized tree and the over-parameterized Gradient Boosting model seem to fit training noise and degrade. This is the canonical behavior for data that looks like a random walk and is a property of the data, not of the architecture used. Both reinforcement learning and feature engineering proved more important than any sort of model exoticness on this task: the Double DQN agent, our only formulation that operates directly on the lag features, was the only configuration that reported a positive average return on the daily horizon, and it does so because its reward function is cumulative and it directly optimizes that reward function rather than the point-wise prediction error. The decision-making framing thus appears to be more natural for OHLCV data than the price-prediction framing.\u003c/p\u003e \u003cp\u003eOn the quantum side, after fixing the broken-gradient bug we found our QNN, QLSTM and QDQN trained as expected; however at far lower numbers of parameters (24 quantum angles plus a shallow classical wrapper) than our classical baselines, and the performance does not surpass their classical analogues on this data. We also see that our QNN at least trains to a degenerative fixed point on the intraday data: when the inherent signal-to-noise ratio is too low for any model to detect, the inductive bias of the model class is largely irrelevant. These results also serve as a cautionary note for quantum-finance papers which report very positive R\u0026sup2; for intraday returns without stating how they account for same-bar leakage and gradient-flow detachment; our own pre-correction notebooks reported similarly optimistic numbers, and they were artefacts of these issues.\u003c/p\u003e \u003cp\u003eThere are a few obvious areas for improvement in the present study. The limits we placed on the quantum simulations \u0026mdash; four qubits, three layers deep \u0026mdash; are due to per-sample CPU simulation time, and so we believe there is a lot of scope for improvement in terms of expressivity by performing larger experiments either on dedicated hardware accelerators or on real NISQ devices; this is therefore left for future work (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSrivastava et al. 2023\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDoosti et al. 2024\u003c/span\u003e). The trading agents were trained on subsampled data because of the same wall-clock constraint. The universe is composed of eleven diverse tickers, but it is still much smaller than a full equity universe. The evaluation consists of one chronological hold-out and, in order to further strengthen the conclusions, it would be worthwhile carrying out a multi-period rolling-window evaluation. Future directions to explore will include hybrid classical-quantum architectures with deeper circuits (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eQi et al. 2024\u003c/span\u003e; \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eBathala et al. 2025\u003c/span\u003e), improved data encoding schemes, and an evaluation across a wider range of market regimes. In summary, the outcome of this work is that variational quantum machine learning, as it is known today, is a promising yet not definitive tool to address stock market prediction; a careful experimental design \u0026mdash; accurate lag features, normalization only on the training set, chronological splits (\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eHasanov et al. 2022\u003c/span\u003e), gradient-flow correctness and realistic transaction costs \u0026mdash; is no less relevant than the choice between a classical or a quantum algorithm.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting Interests\u003c/h2\u003e \u003cp\u003eThe authors have no relevant financial or non-financial interests to disclose. The authors have no competing interests to declare that are relevant to the content of this article.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eEthics Approval\u003c/h2\u003e \u003cp\u003eNot applicable. This study does not involve human participants, human data or animal subjects.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eClinical Trial Number\u003c/h2\u003e \u003cp\u003eClinical trial number: not applicable.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eConsent to Participate\u003c/h2\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent for Publication\u003c/strong\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThe authors did not receive support from any organization for the submitted work. No funds, grants, or other support were received.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eP.S. conceived the study, designed the experimental framework and led the implementation of the quantum models (QNN, QLSTM and QDQN), including the gradient-flow correction in the PennyLane\u0026ndash;PyTorch hybrid pipeline. P.S. and K.S. developed the leakage-free feature engineering pipeline and the chronological train/test splitting infrastructure used by all models. K.S. implemented the classical machine learning baselines (Decision Tree, Ridge regression and Gradient Boosting) and ran the corresponding experiments. T.V. implemented the deep learning models (ANN and LSTM) and produced the multi-timeframe comparison (1-minute, 5-minute and daily horizons). V.S. implemented the Double Deep Q-Network reinforcement learning agent, designed the trading environment, transaction-cost model and reward function, and produced the per-ticker trading evaluations. P.S., K.S., T.V. and V.S. jointly prepared all figures and tables. P.S. wrote the main manuscript text. V.J. supervised the work, reviewed the methodology, advised on the experimental design and interpretation of results, and provided critical revisions to the manuscript. All authors reviewed and approved the final manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets analysed during the current study consist of historical OHLCV data for eleven large-cap U.S. equities \u0026mdash; AAPL, AMZN, DIS, GOOGL, IBM, KO, META, MSFT, NVDA, SBUX and TSLA \u0026mdash; at one-minute, five-minute and daily granularities. The raw data are publicly available from Yahoo Finance (https://finance.yahoo.com/) and were retrieved using the yfinance Python library. The processed datasets, the leakage-free feature engineering pipeline, the trained model artefacts and the analysis code that support the findings of this study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAntad S, Khandelwal S, Khandelwal A, Khandare R, Khandave P, Khangar D, Khanke R (2023) Stock price prediction website using linear regression \u0026mdash; a machine learning algorithm. ITM Web of Conferences 56\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAtesongun A, Gulsen M (2024) A hybrid forecasting structure based on ARIMA and artificial neural network models. 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BCP Business Management 38:3383\u0026ndash;3388\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXiao J, Deng T, Bi S (2024) Comparative analysis of LSTM, GRU, and transformer models for stock price prediction. \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ehttps://arxiv.org/abs/2411.05790\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Quantum machine learning, Variational quantum circuits, Stock price prediction, Deep reinforcement learning, LSTM, OHLCV data","lastPublishedDoi":"10.21203/rs.3.rs-9653068/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9653068/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eStock price prediction remains a hard problem because financial time series are noisy, non-stationary and nonlinear. Although the literature is large, no single learning paradigm has shown sustained superiority across market regimes. We present a unified comparison of classical machine learning, deep learning, deep reinforcement learning and quantum machine learning on stock prediction and trading from OHLCV data, with greater emphasis on quantum models. Decision Tree, Ridge regression and Gradient Boosting are first developed; the comparison is then extended to Artificial Neural Network (ANN) and Long Short-Term Memory (LSTM). A Deep Q-Network (DQN) trading agent is also implemented. The same models are then re-implemented on variational quantum circuits, giving rise to Quantum Neural Network (QNN), Quantum LSTM (QLSTM) and Quantum DQN (QDQN). All models are trained and evaluated on the same dataset of 209,498 one-minute bars and approximately 27,500 daily bars across eleven liquid U.S. equities, under an identical leakage-free feature pipeline. Evaluation uses RMSE, MAE, directional accuracy, cumulative return and Sharpe ratio. On one-minute intraday data, returns are largely indistinguishable from a near-random walk and no model beats the naive baseline. On the daily horizon, deep learning models show small but consistent improvements; the quantum models perform comparably to classical counterparts at a fraction of the parameter count. The classical DQN delivers a positive average return across tickers, while the buy-and-hold strategy and the QDQN agent under-perform. Overall, near-term variational quantum circuits do not deliver a clear quantum advantage on this task, and careful experimental design matters more than model exoticness.\u003c/p\u003e","manuscriptTitle":"Stock Prediction and Trading from OHLCV Data: A Quantum- Enhanced Learning-Based Comparison","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-14 08:28:56","doi":"10.21203/rs.3.rs-9653068/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a22afdf0-6a2a-4d89-adbd-67f8aa5f5c91","owner":[],"postedDate":"May 14th, 2026","published":true,"recentEditorialEvents":[{"type":"editorAssigned","content":"","date":"2026-05-18T15:26:58+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-05-12T08:33:58+00:00","index":"","fulltext":""},{"type":"submitted","content":"Quantum Machine Intelligence","date":"2026-05-08T10:48:24+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-05-14T08:28:57+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-14 08:28:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9653068","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9653068","identity":"rs-9653068","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}