Improving quantum-to-classical data decoding using optimized quantum wavelet transform

One of the challenges facing current noisy-intermediate-scale-quantum devices 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 their temporal complexity (circuit depth and execution time), spatial complexity (total gate count), and accuracy (fidelity/similarity) in comparison to existing Q2C techniques. Experimental evaluations of the proposed Q2C methods are performed on a 27-qubit state-of-the-art quantum computing device from IBM Quantum using real high-resolution multispectral images. The proposed QHT-based Q2C method achieved up to \(15\times\) higher space efficiency than the QFT-based Q2C method, while the proposed zero-depth method achieved up to 14% and 78% improvements in execution time compared to conventional Q2C and QFT-based Q2C, respectively.