近日，德国柏林自由大学的Jens Eisert&Yihui Quek及其研究团队取得一项新进展。经过不懈努力，他们提出量子错误缓解限制的指数级更严格界限。相关研究成果已于2024年7月25日在国际知名学术期刊《自然—物理学》上发表。
然而，在这项研究中，该研究团队发现了在更大系统尺寸下量子噪声能够被有效“撤销”的程度存在显著限制。该研究提出的框架严格涵盖了当前广泛使用的主要错误缓解方案。通过将错误缓解与统计推理问题相结合，研究表明，即便在电路深度与当前实验相当的情况下，最坏情况下估计无噪声观测值的期望值（这是错误缓解的主要任务）也需要超多项式的样本数量。
值得注意的是，该研究的构造揭示出，噪声引发的混乱可能在比之前预期的更浅的指数级深度上发生。此外，噪声还通过限制量子机器学习中的核估计对其他近期应用造成影响，导致变分量子算法中更早出现噪声诱导的贫瘠高原现象，并排除了在存在噪声的情况下估计期望值或制备哈密顿函数基态时实现指数量子加速的可能性。
据悉，量子错误缓解已被提出作为一种手段，旨在对抗近期量子计算中出现的不期望且不可避免的错误，而无需投入容错方案所需的大量资源。近期，错误缓解已成功应用于短期应用中，有效降低了噪声水平。
附：英文原文
Title: Exponentially tighter bounds on limitations of quantum error mitigation
Author: Quek, Yihui, Stilck Frana, Daniel, Khatri, Sumeet, Meyer, Johannes Jakob, Eisert, Jens
Issue&Volume: 2024-07-25
Abstract: Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault-tolerant schemes. Recently, error mitigation has been successfully applied to reduce noise in near-term applications. In this work, however, we identify strong limitations to the degree to which quantum noise can be effectively ‘undone’ for larger system sizes. Our framework rigorously captures large classes of error-mitigation schemes in use today. By relating error mitigation to a statistical inference problem, we show that even at shallow circuit depths comparable to those of current experiments, a superpolynomial number of samples is needed in the worst case to estimate the expectation values of noiseless observables, the principal task of error mitigation. Notably, our construction implies that scrambling due to noise can kick in at exponentially smaller depths than previously thought. Noise also impacts other near-term applications by constraining kernel estimation in quantum machine learning, causing an earlier emergence of noise-induced barren plateaus in variational quantum algorithms and ruling out exponential quantum speed-ups in estimating expectation values in the presence of noise or preparing the ground state of a Hamiltonian.
DOI: 10.1038/s41567-024-02536-7
Source: https://www.nature.com/articles/s41567-024-02536-7