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arXiv 2305.00547quant-ph
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面向构建用于纠错量子传感的连续逻辑算符

Toward Constructing a Continuous Logical Operator for Error-Corrected Quantum Sensing

Cameron Cianci

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AI总结：

针对量子传感需连续信号但Eastin-Knill定理限制容错连续逻辑算符构建的问题，提出连续逻辑z轴旋转设计协议并应用于Steane码，经Knill-Laflamme条件验证其不具容错性，同时指出该方法在更多或更大距离量子比特编码中有望成功。

摘要：

长期以来，纠错一直被认为可将量子传感器的灵敏度拓展至海森堡极限。然而，逻辑量子比特上的操作仅能通过由Clifford+T等有限尺寸门构成的通用门组来执行。尽管这些逻辑门组可实现通用量子计算，但其有限的门尺寸给量子传感带来了问题——因为在Ramsey测量协议等传感方案中，信号必须连续作用。构建连续逻辑算符的难点源于Eastin-Knill定理，该定理指出连续信号无法同时具备对局部错误的容错性和横向性。由于在噪声环境下逼近海森堡极限需要纠错，因此探索如何构建容错连续算符至关重要。本文提出了一种设计连续逻辑z轴旋转的协议，并将其应用于Steane码（Steane Code）。研究采用Knill-Laflamme条件分析了所设计算符的容错性，结果表明所构建的对角幺正算符不具备容错性，其唯一原因是中间量子比特存在发生X错误的可能性。不过，本文展示的方法有望在更多量子比特的编码（如Shor码、距离为3的表面码、[15,1,3]码）或更大距离的编码（如[11,1,5]码）中取得成功。

英文摘要：

Error correction has long been suggested to extend the sensitivity of quantum sensors into the Heisenberg Limit. However, operations on logical qubits are only performed through universal gate sets consisting of finite-sized gates such as Clifford+T. Although these logical gate sets allow for universal quantum computation, the finite gate sizes present a problem for quantum sensing, since in sensing protocols, such as the Ramsey measurement protocol, the signal must act continuously. The difficulty in constructing a continuous logical operator comes from the Eastin-Knill theorem, which prevents a continuous signal from being both fault tolerant to local errors and transverse. Since error correction is needed to approach the Heisenberg Limit in a noisy environment, it is important to explore how to construct fault-tolerant continuous operators. In this paper, a protocol to design continuous logical z-rotations is proposed and applied to the Steane Code. The fault tolerance of the designed operator is investigated using the Knill-Laflamme conditions. The Knill-Laflamme conditions indicate that the diagonal unitary operator constructed cannot be fault tolerant solely due to the possibilities of X errors on the middle qubit. The approach demonstrated throughout this paper may, however, find success in codes with more qubits such as the Shor code, distance 3 surface code, [15,1,3] code, or codes with a larger distance such as the [11,1,5] code.

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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