Quantum Query Complexity for Nonstandard Oracles with Tight Bounds and Tradeoffs Beyond Grover

Quantum Query Complexity for Nonstandard Oracles with Tight Bounds and Tradeoffs Beyond Grover | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 19 December 2025 V1 Latest version Share on Quantum Query Complexity for Nonstandard Oracles with Tight Bounds and Tradeoffs Beyond Grover Author : Yalla Jnan Devi Satya Prasad 0009-0000-6343-3733 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176616158.89278653/v1 249 views 149 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Quantum query complexity underpins much of our understanding of quantum speedups, yet nearly all existing lower and upper bounds are derived for simple Boolean oracles. Many practical tasks-noisy database search, stochastic optimization, adaptive learning, and time-varying systems-are best modeled by richer oracle classes. This paper systematically extends quantum query complexity theory to four non-standard oracle models: (1) stochastic oracles that return random outputs drawn from a distribution; (2) multi-solution oracles encoding a solution set of size k; (3) time-dependent oracles whose internal state evolves between queries; and (4) relational oracles encoding structured constraints rather than simple membership. Using generalized adversary methods, polynomial method techniques, and hybrid arguments, we derive tight (up to polylog factors) lower bounds for each model and construct matching algorithms where possible. For instance, we show that searching for any one of k marked items in an unstructured database still admits a Grover-like quadratic speedup, but with optimal complexity Θ(N/k), and that stochastic noise in oracle outputs degrades the advantage gracefully as a function of the noise parameter. For certain time-dependent and relational models, we prove that no better-than-classical speedup is possible, clarifying the limits of quantum advantage in adaptive settings. These results provide a more realistic foundation for quantum algorithms targeting noisy search, stochastic optimization, and constraint satisfaction, and they highlight the precise structural features that enable or preclude query-based quantum speedups. Supplementary Material File (quantum query complexity for non-standard oracles.pdf) Download 796.93 KB Information & Authors Information Version history V1 Version 1 19 December 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords computer algorithms computer science deep learning machine learning quantum ai quantum algorithms quantum computing quantum machine learning Authors Affiliations Yalla Jnan Devi Satya Prasad 0009-0000-6343-3733 [email protected] IQ Leap Pvt Ltd View all articles by this author Metrics & Citations Metrics Article Usage 249 views 149 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Yalla Jnan Devi Satya Prasad. Quantum Query Complexity for Nonstandard Oracles with Tight Bounds and Tradeoffs Beyond Grover. Authorea . 19 December 2025. 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