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arXiv 1808.05232quant-phcond-mat.dis-nncond-mat.quant-gasphysics.comp-ph
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量子计算经典模拟的神经网络态

Neural-network states for the classical simulation of quantum computing

Bjarni Jónsson, Bela Bauer, Giuseppe Carleo

摘要:

用经典资源模拟量子算法通常需要指数资源。然而,启发式的经典方法往往是非常有效的近似模拟特殊的电路结构,例如有限的纠缠,或基于一维几何形状。本文介绍了一种基于神经网络量子态(NQS)表示的一般量子线路模拟的经典方法。考虑到一组通用的量子门,我们推导出规则,精确地应用单量子比特和双量子比特的Z旋转NQS,而我们提供了一个学习计划,以近似阿达玛门的行动。结果示出的Hadamard和傅立叶变换的纠缠初始状态的系统大小和总电路深度超过目前可以模拟与国家的最先进的蛮力技术。基于限制玻尔兹曼机的神经网络状态的整体精度是令人满意的,并提供了一个经典的路线来模拟高度纠缠的电路。在考虑的测试情况下,我们发现,我们的经典模拟是量子模拟的影响,在硬件中的非相干噪声水平约$10^{-3}$每门。

英文摘要:

Simulating quantum algorithms with classical resources generally requires exponential resources. However, heuristic classical approaches are often very efficient in approximately simulating special circuit structures, for example with limited entanglement, or based on one-dimensional geometries. Here we introduce a classical approach to the simulation of general quantum circuits based on neural-network quantum states (NQS) representations. Considering a set of universal quantum gates, we derive rules for exactly applying single-qubit and two-qubit Z rotations to NQS, whereas we provide a learning scheme to approximate the action of Hadamard gates. Results are shown for the Hadamard and Fourier transform of entangled initial states for systems sizes and total circuit depths exceeding what can be currently simulated with state-of-the-art brute-force techniques. The overall accuracy obtained by the neural-network states based on Restricted Boltzmann machines is satisfactory, and offers a classical route to simulating highly-entangled circuits. In the test cases considered, we find that our classical simulations are comparable to quantum simulations affected by an incoherent noise level in the hardware of about $10^{-3}$ per gate.

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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