标题： 量子计算的经典模拟的神经网络状态 显示英文标题

标题： Neural-network states for the classical simulation of quantum computing

摘要： 用经典资源模拟量子算法通常需要指数级的资源。 然而，启发式的经典方法在近似模拟特定电路结构时通常非常高效，例如具有有限纠缠或基于一维几何结构的电路。 在这里，我们介绍了一种基于神经网络量子态（NQS）表示的经典方法，用于模拟一般的量子电路。 考虑到一组通用的量子门，我们推导了将单量子比特和双量子比特Z旋转精确应用于NQS的规则，而我们提供了一个学习方案来近似哈达玛门的作用。 结果展示了对于系统尺寸和总电路深度超过当前最先进的暴力技术所能模拟的纠缠初始状态的哈达玛变换和傅里叶变换。 基于受限玻尔兹曼机的神经网络态所获得的整体准确性是令人满意的，并为模拟高度纠缠的电路提供了一条经典路径。 在所考虑的测试案例中，我们发现我们的经典模拟与硬件中每门约有$10^{-3}$的非相干噪声水平影响的量子模拟相当。 显示英文摘要

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.