Quantifying fermionic nonlinearity of quantum circuits
Quantifying fermionic nonlinearity of quantum circuits
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DOI：
10.1103/physrevresearch.4.043100
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发表时间：
2021-11
影响因子：
4.2
通讯作者：
Shigeo Hakkaku;Yuichiro Tashima;K. Mitarai;W. Mizukami;K. Fujii
中科院分区：
文献类型：
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作者：
Shigeo Hakkaku;Yuichiro Tashima;K. Mitarai;W. Mizukami;K. Fujii
变分量子算法（VQA）被认为是在有噪声的中尺度量子（NISQ）器件上证明量子优势的最有前途的方法之一。然而，目前还不清楚VQA是否可以保持量子优势下的NISQ器件的固有噪声，这恶化了量子。在这里，我们提出了一个措施，称为费米子非线性，量化的经典模拟量子电路设计用于模拟费米子哈密顿。具体地说，我们构造了一个基于费米线性光学的经典可模拟性的Monte Carlo型经典算法，其采样开销由费米非线性表征。作为这些技术的演示，我们计算了在退相噪声下由四个费米子模产生的旋转门的费米子非线性的上界。此外，我们还估计了在退相噪声作用下，氢链的幺正耦合团簇单量子电路和双量子电路的采样代价。我们发现，根据错误概率和原子间距，有区域的费米子非线性变得非常小或统一，因此电路是经典模拟。我们相信，我们的方法和结果有助于设计量子电路的费米系统与潜在的量子优势。
Variational quantum algorithms (VQAs) have been proposed as one of the most promising approaches to demonstrate quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, it has been unclear whether VQAs can maintain quantum advantage under the intrinsic noise of the NISQ devices, which deteriorates the quantumness. Here we propose a measure, called fermionic nonlinearity, to quantify the classical simulatability of quantum circuits designed for simulating fermionic Hamiltonians. Specifically, we construct a Monte Carlo type classical algorithm based on the classical simulatability of fermionic linear optics, whose sampling overhead is characterized by the fermionic nonlinearity. As a demonstration of these techniques, we calculate the upper bound of the fermionic nonlinearity of a rotation gate generated by four fermionic modes under the dephasing noise. Moreover, we estimate the sampling costs of the unitary coupled cluster singles and doubles quantum circuits for hydrogen chains subject to the dephasing noise. We find that, depending on the error probability and atomic spacing, there are regions where the fermionic nonlinearity becomes very small or unity, and hence the circuits are classically simulatable. We believe that our method and results help to design quantum circuits for fermionic systems with potential quantum advantages.