Randomized semi-quantum matrix processing

IF 6.6 1区 物理与天体物理 Q1 PHYSICS, APPLIED
Allan Tosta, Thais de Lima Silva, Giancarlo Camilo, Leandro Aolita
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Abstract

We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over the Chebyshev approximation of the target function while keeping the matrix oracle quantum, and is assisted by a variant of the Hadamard test that removes the need for post-selection. The resulting statistical overhead is similar to the fully quantum case and does not incur any circuit depth degradation. On the contrary, the average circuit depth is shown to get smaller, yielding equivalent reductions in noise sensitivity, as explicitly shown for depolarizing noise and coherent errors. We apply our technique to partition-function estimation, linear system solvers, and ground-state energy estimation. For these cases, we prove advantages on average depths, including quadratic speed-ups on costly parameters and even the removal of the approximation-error dependence.

Abstract Image

随机半量子矩阵处理
与标准量子奇异值变换相比,我们提出的量子-经典混合框架更适合早期容错量子硬件模拟通用矩阵函数。该方法基于目标函数的切比雪夫近似的随机化,同时保持矩阵甲骨文的量子化,并通过哈达玛检验的变体辅助,消除了后选择的需要。由此产生的统计开销与全量子情况类似,不会造成任何电路深度下降。相反,平均电路深度会变小,噪声灵敏度也会相应降低,这一点在去极化噪声和相干误差中得到了明确体现。我们将我们的技术应用于分区函数估计、线性系统求解器和基态能量估计。在这些情况下,我们证明了平均深度的优势,包括对昂贵参数的二次加速,甚至消除了对近似误差的依赖。
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来源期刊
npj Quantum Information
npj Quantum Information Computer Science-Computer Science (miscellaneous)
CiteScore
13.70
自引率
3.90%
发文量
130
审稿时长
29 weeks
期刊介绍: The scope of npj Quantum Information spans across all relevant disciplines, fields, approaches and levels and so considers outstanding work ranging from fundamental research to applications and technologies.
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