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arXiv 2211.00697quant-phcs.ITmath.IT
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容错量子计算的一个逆命题

A Converse for Fault-tolerant Quantum Computation

Uthirakalyani G, Anuj K. Nayak, Avhishek Chatterjee

备注：
Some changes were made, and results changed in the lower order term only (scaling factor added), Edited license
发表信息：
Quantum 7, 1087 (2023)
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AI总结：

该研究通过关联容错量子计算与有限块长量子通信问题，推导了含酉算子的大类操作ε-精度实现的冗余度下界，在亚指数深度等场景下更紧，还严格缩小了非退化噪声阈值上界并可推广至非独立同分布噪声情形。

摘要：

随着容错量子计算技术不断进步，我们自然会问：冗余度的基本下界是多少？本文中，我们针对包含酉算子在内的一大类操作的ε-精度实现，推导了所需冗余度的一个下界。对于具有实际意义的亚指数深度、亚线性门规模的情形，我们得到的冗余度下界比已知下界更紧。我们通过将容错计算与一类精度要求满足联合约束的有限块长量子通信问题建立关联，得到了该下界。本文得到的冗余度下界，使得非退化噪声的噪声阈值上界严格变小。我们的下界可直接推广到门输出端噪声非独立同分布、但跨门噪声独立同分布的情形。

英文摘要：

As techniques for fault-tolerant quantum computation keep improving, it is natural to ask: what is the fundamental lower bound on redundancy? In this paper, we obtain a lower bound on the redundancy required for $ε$-accurate implementation of a large class of operations that includes unitary operators. For the practically relevant case of sub-exponential depth and sub-linear gate size, our bound on redundancy is tighter than the known lower bounds. We obtain this bound by connecting fault-tolerant computation with a set of finite blocklength quantum communication problems whose accuracy requirements satisfy a joint constraint. The lower bound on redundancy obtained here leads to a strictly smaller upper bound on the noise threshold for non-degradable noise. Our bound directly extends to the case where noise at the outputs of a gate are non-i.i.d. but noise across gates are i.i.d.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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