Improving Quantum-to-Classical Data Decoding using Optimized Quantum Wavelet Transform

One of the challenges facing current Noisy-Intermediate-Scale-Quantum devices (NISQ) is achieving efficient quantum circuit measurement or readout. The process of extracting classical data from the quantum domain, termed in this work as quantum-to-classical (Q2C) data decoding, generally incurs significant overhead, since the quantum circuit needs to be sampled repeatedly to obtain useful data readout. In this paper, we propose and evaluate time-efficient and depth-optimized Q2C methods based on the multidimensional, multilevel-decomposable, quantum wavelet transform (QWT) whose packet and pyramidal forms are leveraged and optimized. We also propose a zero-depth technique that uses selective placement of measurement gates to perform the QWT operation. To demonstrate their efficiency, the proposed techniques are quantitatively evaluated in terms of execution time, circuit depth, and accuracy in comparison to existing Q2C techniques. Experimental evaluations of the proposed Q2C methods are performed using real high-resolution multispectral images on a 27-qubit state-of-the-art quantum computing device from IBM Quantum.