2026/08/04 by Chao Wang, Xi-Ning Zhuang, Menghan Dou +2
Physics and Astronomy · #quant-ph
This article supersedes arXiv:2604.02874. The present work substantially reformulates the previous framework, replaces the coherent frequency implementation with a polynomial eigenvalue transformation, and establishes access-dependent approximation and query-complexity results
arxiv created 2026/08/04 · arxiv updated 2026/08/06
We study quantum implementations of the contraction exp(-T Hα) for H=H^†\succeq0 and α>0. Poisson summation provides an exact target--alias--tail decomposition whose Fourier samples are compiled classically into a single Chebyshev polynomial, so the quantum circuit uses polynomial eigenvalue transformation rather than a frequency linear combination of unitaries. We compare block encodings of H/\normH and of the shifted signal 2H/\normH-I. Under ordinary single-sequence QSVT, parity forces the former to use an even extension, which is entire only for even positive integers. An exact quadratic lift for the shifted signal makes every positive integer entire and improves the fixed-scale approximation error for noninteger powers from Θ(d-α) to Θ(d-2α) within the stated access and parity classes. We derive matching degree bounds in the large-scale fixed-error and fixed-scale high-precision limits, including the output-normalization overhead ur. Nearest-neighbor Laplacians give a unit-normalized shifted signal. We further establish a noncommutative Weyl--Poisson identity compatible with LCHS quadrature, and use the same polynomial construction to implement controlled dissipative families in amplitude--phase separation.