论文标题
易于断层量子计算的相反
A Converse for Fault-tolerant Quantum Computation
论文作者
论文摘要
随着易于故障量子计算的技术不断改进，自然要问：冗余的基本下限是什么？在本文中，我们获得了$ε$准确实施包括统一运营商的大型操作所需的冗余。对于次指数深度和亚线性栅极大小的实际相关情况，我们对冗余的界限比已知的下限更紧。我们通过将易耐故障计算与一组有限的区块长度量子通信问题连接起来来获得这种束缚，这些量子通信问题的准确性要求满足关节约束。此处获得的冗余上的下限导致噪声阈值严格较小的上限，无法降解噪声。我们的界限直接延伸到门口输出处的噪声为非i.i.d的情况。但是跨门的噪音是I.I.D。
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.
