Universal noise-precision relations in variational quantum algorithms
Universal noise-precision relations in variational quantum algorithms
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DOI：
10.1103/physrevresearch.5.023025
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发表时间：
2021-06
影响因子：
4.2
通讯作者：
Kosuke Ito;W. Mizukami;K. Fujii
中科院分区：
文献类型：
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作者：
Kosuke Ito;W. Mizukami;K. Fujii
变分量子算法（VQAs）有望成为近期噪声量子计算机的实际应用。尽管噪声的影响至关重要地决定了VQA是否有效，但VQA的启发式性质使其难以建立分析理论。由于在经典计算机上对噪声量子计算机进行数值模拟的工作量很大，而且仅限于小尺度问题，因此对噪声影响的解析估计对于寻找量子优势是迫切需要的。在本文中，我们建立了由噪声引起的vqa成本函数误差的解析估计。该估计适用于高斯噪声下的任意典型vqa，等效于一类随机噪声模型。值得注意的是，该模型中包含了去极化噪声。因此，我们得到了噪声级的估计，以保证所需的精度。我们的公式显示了代价函数的Hessian、目标算子的频谱和ansatz的几何形状如何影响对噪声的灵敏度。这种见解意味着成本函数的可训练性和噪声弹性之间的权衡关系。我们也得到了粗略的估计，不需要成本函数的详细信息就可以很容易地计算出来。作为该公式应用的一个亮点，我们提出了一种不同于外推和概率误差抵消的量子误差缓解方法。
Variational quantum algorithms (VQAs) are expected to become a practical application of near-term noisy quantum computers. Although the effect of the noise crucially determines whether a VQA works or not, the heuristic nature of VQAs makes it difficult to establish analytic theories. Analytic estimations of the impact of the noise are urgent for searching for quantum advantages, as numerical simulations of noisy quantum computers on classical computers are heavy and quite limited to small scale problems. In this paper, we establish analytic estimations of the error in the cost function of VQAs due to the noise. The estimations are applicable to any typical VQAs under the Gaussian noise, which is equivalent to a class of stochastic noise models. Notably, the depolarizing noise is included in this model. As a result, we obtain estimations of the noise level to guarantee a required precision. Our formulae show how the Hessian of the cost function, the spectrum of the target operator, and the geometry of the ansatz affect the sensitivity to the noise. This insight implies trade-off relations between the trainability and the noise resilience of the cost function. We also obtain rough estimations which can be easily calculated without detailed information of the cost function. As a highlight of the applications of the formula, we propose a quantum error mitigation method which is different from the extrapolation and the probabilistic error cancellation.