论文标题
在一个维
Efficient classical simulation of noisy random quantum circuits in one dimension
论文作者
论文摘要
了解嘈杂的中等规模量子（NISQ）设备的计算能力对于量子信息科学具有基本和实际重要性。在这里，我们解决了一个问题，即错误纠正的嘈杂量子计算机是否可以比古典计算机提供计算优势。具体而言，我们在一个维度（或1D Noisy RCS）中研究嘈杂的随机电路采样，作为探索噪声对噪声量子设备计算功率的影响的简单模型。特别是，我们通过矩阵产品运算符（MPO）模拟1D噪声随机量子电路的实时动力学，并通过使用度量标准来表征1D噪声量子系统的计算能力，我们称为MPO纠缠熵。之所以选择后一个度量，是因为它决定了经典MPO模拟的成本。我们从数值上证明，对于我们考虑的两个QUITANT错误率，存在一个特征性的系统大小，添加更多的量子位并不会带来1D噪声系统经典MPO模拟成本的指数增长。具体而言，我们表明，在特征系统大小上方，有一个最佳的电路深度，与系统大小无关，其中MPO纠缠熵是最大化的。最重要的是，最大可实现的MPO纠缠熵是由仅取决于门错误率而不取决于系统大小的常数。我们还提供了启发式分析，以获取最大可实现的MPO纠缠熵的缩放，这是门错误率的函数。所获得的缩放表明，尽管MPO模拟的成本在高于某个特征系统大小的系统大小中并未成倍增加，但它确实会随着栅极误差率降低而成倍增加，即使在最新的超级计算机中，也可能使经典仿真实际上也不可行。
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.
