Efficient classical simulation of noisy random quantum circuits in one dimension
Efficient classical simulation of noisy random quantum circuits in one dimension
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DOI：
10.22331/q-2020-09-11-318
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发表时间：
2020-09-08
期刊：
影响因子：
6.4
通讯作者：
Fefferman, Bill
中科院分区：
文献类型：
--
作者：
Noh, Kyungjoo;Jiang, Liang;Fefferman, Bill
了解噪声中尺度量子（NISQ）器件的计算能力对量子信息科学具有重要的基础和实际意义。在这里，我们解决了错误未校正的噪声量子计算机是否可以提供优于经典计算机的计算优势的问题。具体来说，我们研究了一维噪声随机电路采样（或1D噪声RCS）作为探索噪声对噪声量子器件计算能力影响的简单模型。特别是，我们通过矩阵积算符（MPO）模拟了一维噪声随机量子电路的实时动力学，并通过称为MPO纠缠熵的度量来表征一维噪声量子系统的计算能力。选择后一个指标是因为它决定了经典MPO模拟的成本。我们通过数值证明，对于我们所考虑的双量子比特门错误率，存在一个特征系统大小，在该系统大小之上，增加更多的量子比特不会导致一维噪声系统的经典MPO模拟成本呈指数增长。具体来说，我们证明了在特征系统尺寸以上，存在一个与系统尺寸无关的最佳电路深度，其中MPO纠缠熵最大化。最重要的是，可实现的最大MPO纠缠熵由一个常数限定，该常数仅取决于门错误率，而不取决于系统大小。我们还提供了一个启发式分析，以获得最大可实现的MPO纠缠熵作为门错误率的函数的缩放。所获得的缩放表明，尽管MPO模拟的成本在系统规模超过某一特征系统规模时不会呈指数级增长，但随着门错误率的降低，它会呈指数级增长，这可能使经典模拟即使在最先进的超级计算机上也不可行。
Understanding the computational power of noisy intermediate-scale quantum (NISQ) devices is of both fundamental and practical importance to quantum information science. Here, we address the question of whether error-uncorrected noisy quantum computers can provide computational advantage over classical computers. Specifically, we study noisy random circuit sampling in one dimension (or 1D noisy RCS) as a simple model for exploring the effects of noise on the computational power of a noisy quantum device. In particular, we simulate the real-time dynamics of 1D noisy random quantum circuits via matrix product operators (MPOs) and characterize the computational power of the 1D noisy quantum system by using a metric we call MPO entanglement entropy. The latter metric is chosen because it determines the cost of classical MPO simulation. We numerically demonstrate that for the two-qubit gate error rates we considered, there exists a characteristic system size above which adding more qubits does not bring about an exponential growth of the cost of classical MPO simulation of 1D noisy systems. Specifically, we show that above the characteristic system size, there is an optimal circuit depth, independent of the system size, where the MPO entanglement entropy is maximized. Most importantly, the maximum achievable MPO entanglement entropy is bounded by a constant that depends only on the gate error rate, not on the system size. We also provide a heuristic analysis to get the scaling of the maximum achievable MPO entanglement entropy as a function of the gate error rate. The obtained scaling suggests that although the cost of MPO simulation does not increase exponentially in the system size above a certain characteristic system size, it does increase exponentially as the gate error rate decreases, possibly making classical simulation practically not feasible even with state-of-the-art supercomputers.