arXiv 2002.077302020-02quant-phcond-mat.str-el

是什么限制了量子计算机的模拟？

What limits the simulation of quantum computers?

Yiqing Zhou, E. Miles Stoudenmire, Xavier Waintal

备注：: New data added, 14 figures
发表信息：: Phys. Rev. X 10, 041038 (2020)
DOI：: 10.1103/PhysRevX.10.041038

摘要：

有用的量子计算机必须非常难以经典模拟;否则经典计算机可以用于量子计算机的应用。完美的量子计算机无疑是指数级难以模拟的：所需的经典资源随着量子位数$N$或电路深度$D$呈指数级增长。然而，真正的量子计算设备的特征在于指数衰减的保真度$\mathcal{F} \sim (1-ε)^{ND}$，其中每个操作的错误率$ε$与当前设备的$\approx 1\%$一样小。在这项工作中，我们证明了可以以完美量子计算机所需成本的一小部分来模拟真正的量子计算机。我们的算法使用矩阵乘积态（MPS）压缩量子波函数的表示，非常准确地捕获具有低到中等纠缠的状态。这种压缩引入了有限的错误率$ε$，使得算法紧密地模仿真实量子计算设备的行为。我们的算法的计算时间仅与$N$和$D$线性增加。我们说明了我们的算法与模拟的随机电路的量子位连接在一维和二维晶格。我们发现，$ε$可以减少在一个多项式的成本计算能力下降到最小的错误$ε_\infty$。低于$ε_\infty$要求计算资源随着$ε_\infty/ε$呈指数级增长。对于$N=54$量子位的二维阵列和具有Control-Z门的电路，可以在几个小时内在笔记本电脑上获得比最先进的设备更好的错误率。对于更复杂的门，例如交换门之后是受控旋转，对于类似的计算时间，错误率增加了三倍。

英文摘要：

It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably exponentially difficult to simulate: the classical resources required grow exponentially with the number of qubits $N$ or the depth $D$ of the circuit. Real quantum computing devices, however, are characterized by an exponentially decaying fidelity $\mathcal{F} \sim (1-ε)^{ND}$ with an error rate $ε$ per operation as small as $\approx 1\%$ for current devices. In this work, we demonstrate that real quantum computers can be simulated at a tiny fraction of the cost that would be needed for a perfect quantum computer. Our algorithms compress the representations of quantum wavefunctions using matrix product states (MPS), which capture states with low to moderate entanglement very accurately. This compression introduces a finite error rate $ε$ so that the algorithms closely mimic the behavior of real quantum computing devices. The computing time of our algorithm increases only linearly with $N$ and $D$. We illustrate our algorithms with simulations of random circuits for qubits connected in both one and two dimensional lattices. We find that $ε$ can be decreased at a polynomial cost in computing power down to a minimum error $ε_\infty$. Getting below $ε_\infty$ requires computing resources that increase exponentially with $ε_\infty/ε$. For a two dimensional array of $N=54$ qubits and a circuit with Control-Z gates, error rates better than state-of-the-art devices can be obtained on a laptop in a few hours. For more complex gates such as a swap gate followed by a controlled rotation, the error rate increases by a factor three for similar computing time.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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