Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary $U$ is compiled into a short-depth gate sequence $V$. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence $V$ (i.e., the correct variational parameters) despite various sources of incoherent noise acting during the cost-evaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by a broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM's noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver.

中文翻译：

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变分量子编译的抗噪性

变分混合量子经典算法 (VHQCA) 是利用经典优化来最小化成本函数的近期算法，该成本函数可在量子计算机上进行有效评估。最近，VHQCA 已经被提出用于量子编译，其中一个目标幺正 $U$ 被编译成一个短深度门序列 $V$。在这项工作中，我们报告了这些算法的一种令人惊讶的噪声弹性形式。也就是说，我们发现人们经常学习正确的门序列 $V$（即正确的变分参数），尽管在成本评估电路中存在各种不相干噪声源。我们的主要结果是严格的定理，表明最优变分参数不受大类噪声模型的影响，例如测量噪声、门噪声和泡利通道噪声。此外，我们在 IBM 噪声模拟器上的数值实现在编译量子傅立叶变换、Tofffoli 门和 W 状态准备时展示了弹性。因此，变分量子编译由于其鲁棒性，对于嘈杂的中等规模量子设备实际上可能有用。最后，我们推测这种噪声弹性可能是适用于其他 VHQCA 的普遍现象，例如变分量子特征求解器。