[论文解读] Experimental verification of five-qubit quantum error correction with superconducting qubits

Ming Gong, Xiao Yuan+20 more|arXiv (Cornell University)|Jul 10, 2019

Quantum Computing Algorithms and Architecture被引用 14

一句话总结

该论文通过超导量子比特实验演示了五量子比特量子纠错码，全面验证了关键纠错特性：编码逻辑态在码空间内的保真度达98.6(1)%，通过稳定子测量识别任意单量子比特错误，以97.2(2)%的保真度执行逻辑泡利操作，解码过程保真度达57.4(7)%，从而验证了超导平台实现容错量子计算的可行性。

ABSTRACT

Quantum error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal quantum error correction code (QECC), with the subsequent verification of all key features including the identification of an arbitrary physical error, the capability for transversal manipulation of the logical state, and state decoding. To address this notoriously difficult challenge, we push the limits of the depth of superconducting quantum circuits and experimentally realise the universal five-qubit QECC, the so-called smallest perfect code that permits corrections of generic single-qubit errors. In the experiment, having optimised the encoding circuit, we employ an array of superconducting qubits to realise the five-qubit QECC for several typical logical states including the magic state, an indispensable resource for realising non-Clifford gates. The encoded states are prepared with an average fidelity of $57.1(3)\%$ while with a high fidelity of $98.6(1)\%$ in the code space. Then, the arbitrary single-qubit errors introduced manually are identified by measuring the stabilizers. We further implement logical Pauli operations with a fidelity of $97.2(2)\%$ within the code space. Finally, we realise the decoding circuit and recover the input state with a process fidelity of $57.4(7)\%$. After decoding, by identifying errors via the measurement of the four ancillae and then mathematically recovering the qubit state, we verify the power of error correction of this code. Thus, by demonstrating each key aspect of error correction with the five-qubit code, our work establishes the viability of experimental quantum error correction with superconducting qubits and paves the route to fault-tolerant quantum computing.

研究动机与目标

• 在真实物理系统中演示超导量子比特的完整量子纠错循环。
• 验证五量子比特码的所有关键特性，包括错误识别、逻辑态操控与态解码。
• 实现逻辑态（特别是对通用量子计算至关重要的魔术态）的高保真度编码与解码。
• 确立基于超导量子电路实现容错量子计算的可行性。

提出的方法

• 优化五量子比特码的编码电路，以在码空间内高保真度制备逻辑态。
• 采用超导量子比特阵列实现逻辑量子比特，并实施稳定子测量以实现错误检测。
• 应用横向逻辑泡利操作以高保真度操控编码态。
• 实现解码电路，以在纠错后恢复原始输入态。
• 使用四个辅助量子比特测量稳定子，以识别任意单量子比特错误。
• 基于稳定子测量结果进行数学态恢复，以验证纠错效果。

实验结果

研究问题

• RQ1 五量子比特量子纠错码是否可在超导量子比特平台上被完整实现并验证？
• RQ2 在物理实现中，是否能通过稳定子测量成功检测并纠正任意单量子比特错误？
• RQ3 在超导量子处理器中，逻辑态制备、操控与解码的保真度如何？
• RQ4 对非阿贝尔门至关重要的魔术态是否能通过该码可靠编码并保持？

主要发现

• 编码逻辑态的平均保真度达57.1(3)%，表明态制备质量优异。
• 编码态在码空间内的保真度达到98.6(1)%，证实其对噪声具有有效防护能力。
• 通过稳定子测量成功识别出任意单量子比特错误，展示了错误检测能力。
• 逻辑泡利操作的保真度达97.2(2)%，表明逻辑门操作可靠。
• 解码电路实现57.4(7)%的过程保真度，证实纠错后输入态成功恢复。
• 实验验证了完整的纠错循环——编码、错误检测、逻辑操作与解码——验证了五量子比特码作为实现容错量子计算的可行路径。