具有局部粒子数守恒的量子算法:噪声效应和误差校正

Michael Streif, M. Leib, F. Wudarski, E. Rieffel, Zhihui Wang
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引用次数: 24

摘要

具有局部粒子数守恒的量子电路将量子计算限制在量子比特寄存器的希尔伯特空间的一个子空间中。在无噪声或容错的量子计算中,这些量被保留下来。然而,在存在噪声的情况下,演化的对称性可能会被打破,在计算结束时可能会采样到非有效状态。另一方面,理想情况下对子空间的限制表明,对于保持一般电路不可能实现的对称性的电路,有可能采用更节约资源的误差缓解技术。在此,我们分析了在噪声条件下保持对称子空间的概率,给出了局部去极化噪声的精确公式。我们将这些发现应用于去极化噪声下,对具有局部粒子数守恒对称性的XY-QAOA的对称性鲁棒性进行了基准测试,并将其作为量子交替算子Ansatz的一个特例。我们还分析了编码问题的选择对算法对称性鲁棒性的影响,并讨论了一种简单的自适应比特翻转码,以减少资源来纠正对称性破坏错误。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Quantum algorithms with local particle-number conservation: Noise effects and error correction
Quantum circuits with local particle number conservation (LPNC) restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved. In the presence of noise, however, the evolution's symmetry could be broken and non-valid states could be sampled at the end of the computation. On the other hand, the restriction to a subspace in the ideal case suggest the possibility of more resource efficient error mitigation techniques for circuits preserving symmetries that are not possible for general circuits. Here, we analyze the probability of staying in such symmetry-preserved subspaces under noise, providing an exact formula for local depolarizing noise. We apply our findings to benchmark, under depolarizing noise, the symmetry robustness of XY-QAOA, which has local particle number conserving symmetries, and is a special case of the Quantum Alternating Operator Ansatz. We also analyze the influence of the choice of encoding the problem on the symmetry robustness of the algorithm and discuss a simple adaption of the bit flip code to correct for symmetry-breaking errors with reduced resources.
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