[论文解读] Demonstrating Quantum Error Correction that Extends the Lifetime of Quantum Information

Nissim Ofek, Andrei Petrenko+11 more|arXiv (Cornell University)|Feb 15, 2016

Quantum Computing Algorithms and Architecture参考文献 61被引用 19

一句话总结

该论文展示了一种基于超导谐振腔中猫态的容错量子误差校正（QEC）系统，通过该系统可将逻辑量子比特的寿命延长至超过任一物理组件相干时间。通过实施实时反馈与项目测量，系统实现了320 μs的逻辑量子比特寿命——是Transmon的20倍，且比系统中最佳组件的寿命长10%，标志着首次实验验证了QEC在自然发生错误的情况下超越临界点（break-even point）。

ABSTRACT

The remarkable discovery of Quantum Error Correction (QEC), which can overcome the errors experienced by a bit of quantum information (qubit), was a critical advance that gives hope for eventually realizing practical quantum computers. In principle, a system that implements QEC can actually pass a "break-even" point and preserve quantum information for longer than the lifetime of its constituent parts. Reaching the break-even point, however, has thus far remained an outstanding and challenging goal. Several previous works have demonstrated elements of QEC in NMR, ions, nitrogen vacancy (NV) centers, photons, and superconducting transmons. However, these works primarily illustrate the signatures or scaling properties of QEC codes rather than test the capacity of the system to extend the lifetime of quantum information over time. Here we demonstrate a QEC system that reaches the break-even point by suppressing the natural errors due to energy loss for a qubit logically encoded in superpositions of coherent states, or cat states of a superconducting resonator. Moreover, the experiment implements a full QEC protocol by using real-time feedback to encode, monitor naturally occurring errors, decode, and correct. As measured by full process tomography, the enhanced lifetime of the encoded information is 320 microseconds without any post-selection. This is 20 times greater than that of the system's transmon, over twice as long as an uncorrected logical encoding, and 10% longer than the highest quality element of the system (the resonator's 0, 1 Fock states). Our results illustrate the power of novel, hardware efficient qubit encodings over traditional QEC schemes. Furthermore, they advance the field of experimental error correction from confirming the basic concepts to exploring the metrics that drive system performance and the challenges in implementing a fault-tolerant system.

研究动机与目标

• 证明量子误差校正（QEC）可将量子信息的寿命延长至超过其物理组分的相干时间。
• 在自然退相干条件下，实现包含编码、错误监测与校正的完整QEC协议，并支持实时反馈。
• 实现QEC的“临界点”，即逻辑量子比特寿命超过系统中最佳物理组件的寿命。
• 验证基于超导谐振腔中猫态的硬件高效QEC方案的性能。
• 量化重复误差校正轮次中过程保真度的指数衰减，并通过有效的错误项目测量与校正证明该衰减可被抑制。

提出的方法

• 在超导谐振腔中通过相干态的叠加（猫态）编码逻辑量子比特，利用其内在对称性实现错误检测。
• 使用Transmon量子比特作为辅助量子比特，对错误项目进行重复的实时投影测量，以检测光子丢失事件。
• 实施包含实时反馈的完整QEC协议，实现错误检测后的即时校正，涵盖编码、监测与解码操作。
• 通过完整过程层析成像表征逻辑操作保真度，并追踪编码态随时间的演化。
• 对测量记录实施事后选择与置信度分析，以识别高保真度轨迹，并评估误差校正结果的可靠性。
• 测量在单个误差轨迹（0、1、2或3个错误）条件下的过程保真度，以评估在不同错误率下的校正性能。

实验结果

研究问题

• RQ1 QEC系统能否抑制自然发生的错误（特别是光子丢失），将逻辑量子比特的寿命延长至超过任一物理组件的相干时间？
• RQ2 实时反馈与项目测量是否能使系统超越临界点，即逻辑量子比特寿命超过系统中最佳物理元件的寿命？
• RQ3 QEC过程的保真度在重复校正轮次中如何衰减？这种衰减是否可通过有效的错误项目测量得到抑制？
• RQ4 误差校正的保真度在多大程度上依赖于检测到的错误数量以及测量记录的置信度？
• RQ5 像谐振腔中猫态这样的硬件高效编码方式，是否能在实验环境中实现与传统QEC方案相当甚至更优的性能？

主要发现

• 通过完整过程层析成像测得的逻辑量子比特寿命为320 μs，是Transmon量子比特寿命的20倍，且比谐振腔Fock态相干时间长10%。
• 系统实现了临界点，即逻辑量子比特寿命超过系统中最佳物理组件的寿命，证实了QEC在延长量子信息寿命方面的可行性。
• 通过有效的错误项目测量与实时校正，过程保真度的衰减速率得到抑制，表明QEC可优于未经校正的逻辑编码。
• 对于初始猫态大小 $\bar{n}_0 = 2$，系统在错误校正结果中保持了高置信度，约80%的轨迹在约100 μs后仍为高置信度，得益于后续项目测量的可靠错误验证。
• 在检测到两个错误的轨迹中，过程保真度随时间上升，表明更高的测量记录统计置信度使错误检测的可靠性得到提升。
• 对于 $\bar{n}_0 = 3$，0错误情况的保真度从0.84下降至0.69，而2错误情况的保真度显著上升，证实了测量保真度与记录确认在提升校正可靠性中的关键作用。