Continuous quantum error correction for evolution under time-dependent Hamiltonians
Continuous quantum error correction for evolution under time-dependent Hamiltonians
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DOI：
10.1103/physreva.103.042406
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发表时间：
2021-04-05
影响因子：
2.9
通讯作者：
Whaley, K. B.
中科院分区：
文献类型：
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作者：
Atalaya, J.;Zhang, S.;Whaley, K. B.
我们开发了一个协议，用于连续操作的量子纠错码的保护相干演化由于编码的哈密顿对环境的错误，使用三量子位位翻转码和位翻转错误作为一个典型的例子。为了在真实的时间检测错误，我们过滤的输出信号从连续测量的错误综合征运营商，并使用一个双阈值协议的错误诊断，而错误的纠正是在常规操作。我们优化我们的连续操作协议下的量子存储器和量子退火下的进化，通过最大限度地提高目标和实际的逻辑状态之间的保真度在指定的最终时间。在量子存储器的情况下，我们表明，我们的连续操作协议产生的逻辑错误率略大于使用最佳Wonham滤波器进行错误诊断，同时更容易实现。对于量子退火，我们表明，我们的连续量子纠错协议可以显着减少最终的逻辑状态不忠时，连续测量是足够强的强度相对于时间依赖的哈密顿量。我们还表明，这种连续的量子纠错协议可以减少时间的解决方案相对于从经典的并行化方案获得的值。这些结果表明，在存在编码的含时哈密顿量的情况下，连续实现适合于量子纠错，这为量子模拟和量子退火中的许多应用开辟了可能性。
We develop a protocol for continuous operation of a quantum error correcting code for protection of coherent evolution due to an encoded Hamiltonian against environmental errors, using the three-qubit bit-flip code and bit-flip errors as a canonical example. To detect errors in real time, we filter the output signals from continuous measurement of the error syndrome operators and use a double thresholding protocol for error diagnosis, while correction of errors is done as in the conventional operation. We optimize our continuous operation protocol for evolution under quantum memory and under quantum annealing, by maximizing the fidelity between the target and actual logical states at a specified final time. In the case of quantum memory, we show that our continuous operation protocol yields a logical error rate that is slightly larger than the one obtained from using the optimal Wonham filter for error diagnosis while being simpler to implement. For quantum annealing, we show that our continuous quantum error correction protocol can significantly reduce the final logical state infidelity when the continuous measurements are sufficiently strong relative to the strength of the time-dependent Hamiltonian. We also show that this continuous quantum error correction protocol can reduce the time-to-solution relative to the value obtained from a classical parallelization scheme. These results suggest that a continuous implementation is suitable for quantum error correction in the presence of encoded time-dependent Hamiltonians, opening the possibility of many applications in quantum simulation and quantum annealing.