AI 中文总结
研究非厄米量子绝热算法，通过映射非酉量子电路到局部哈密顿路径提出新框架，解决了直接扩展的赝谱不稳定问题，实现多项式演化时间计算且对微扰鲁棒，确立了赝谱稳定性等关键原则及实用途径。
AI 中文摘要
非厄米系统为量子优化和计算带来新机遇。本文表明非厄米量子绝热算法不仅需要实的、有能隙的谱，还需要稳定的赝谱。我们通过将非酉量子电路映射到局部哈密顿路径提出一个新框架，保留其优化优势和浅深度。费曼 - 基塔耶夫构造的直接非厄米扩展存在严重的赝谱不稳定性，而我们的历史解耦构造产生可控的赝谱和实的、有能隙的谱。利用最大独立集问题的CK基准族，我们展示了多项式演化时间的非厄米绝热计算对微扰具有鲁棒性。我们还讨论了使用带有辅助有损通道的耦合波导的可行光学实现。我们的工作确立了赝谱稳定性以及实的、有能隙的谱作为非厄米量子绝热计算的关键原则和实用途径。
英文摘要
Non-Hermitian systems offer new opportunities for quantum optimization and computation. Here, we show that non-Hermitian quantum adiabatic algorithms require not only a real, gapped spectrum, but also a stable pseudospectrum. We propose a novel framework by mapping non-unitary quantum circuits to local Hamiltonian paths, thereby preserving their optimization advantages and shallow depth. While a direct non-Hermitian extension of the Feynman-Kitaev construction suffers severe pseudospectral instability, our history-decoupled construction yields both a controlled pseudospectrum and a real, gapped spectrum. Using the CK benchmark family of maximum independent set problems, we demonstrate polynomial-evolution-time non-Hermitian adiabatic computation that remains robust against perturbations. We further discuss a feasible optical implementation using coupled waveguides with an auxiliary lossy channel. Our work establishes pseudospectral stability, alongside real, gapped spectra, as key principles and a practical route for non-Hermitian quantum adiabatic computation.
Comments18 pages, 8 figures
