利用结构经典阴影增强量子态重构

IF 8.3 1区 物理与天体物理 Q1 PHYSICS, APPLIED
Zhen Qin, Joseph M. Lukens, Brian T. Kirby, Zhihui Zhu
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引用次数: 0

摘要

虽然经典阴影可以有效地预测关键的量子态特性,但它们对认证量子态层析成像的适用性仍然不确定。在本文中,我们通过引入投影经典阴影(PCS)来解决这一挑战,PCS通过在目标子空间上合并投影步长来扩展标准经典阴影。对于由n个量子比特组成的一般量子态,我们的方法需要至少O(4n)个总状态拷贝才能在重构和真密度矩阵之间的Frobenius范数中实现有界恢复误差,对于秩为r <; 2n的状态,在这两种情况下都满足信息论最优边界,则减少到O(2nr)。对于矩阵积算子状态,我们证明了PCS可以用O(n2)个总状态副本恢复基真状态,改进了先前建立的O(n3)的haar随机界。数值模拟验证了我们的缩放结果,并证明了PCS方法的实用精度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Enhancing quantum state reconstruction with structured classical shadows

Enhancing quantum state reconstruction with structured classical shadows

While classical shadows can efficiently predict key quantum state properties, their suitability for certified quantum state tomography remains uncertain. In this paper, we address this challenge by introducing a projected classical shadow (PCS) that extends the standard classical shadow by incorporating a projection step onto the target subspace. For a general quantum state consisting of n qubits, our method requires a minimum of O(4n) total state copies to achieve a bounded recovery error in the Frobenius norm between the reconstructed and true density matrices, reducing to O(2nr) for states of rank r < 2n—meeting information-theoretic optimal bounds in both cases. For matrix product operator states, we demonstrate that the PCS can recover the ground-truth state with O(n2) total state copies, improving upon the previously established Haar-random bound of O(n3). Numerical simulations validate our scaling results and demonstrate the practical accuracy of the proposed PCS method.

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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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