用广义Ising机模拟量子干涉
Emulating Quantum Interference with Generalized Ising Machines
AI总结：
提出将量子门序列精确映射为概率p-bit网络（复数能量Boltzmann机），通过引入能量实部结合Gibbs采样与Ising机硬件加速，突破量子电路模拟的指数级计算瓶颈。
摘要：
本文的主要目标是提出一种精确且通用的程序，将任何量子门序列映射到概率p-bit（可取值0或1）网络上。前$n$个p-bit代表输入量子比特，其余p-bit代表经过连续门操作后的量子比特。我们可以将此结构视为一个Boltzmann机，其每个状态代表一条从量子比特初始构型到最终构型的Feynman路径。每条此类路径具有复数振幅$ψ$，可对应于复数能量。该能量的实部可用于以常规方式生成Feynman路径样本，而虚部则通过将样本视为复数实体来处理，这与样本均为正数的普通Boltzmann机不同。量子门通常具有纯虚数能量函数，所有构型概率相同，无法利用采样技术。然而，若能通过适当变换在能量函数中引入实部，便可利用Gibbs采样等强大算法以极少样本获得可接受结果，甚至可能摆脱随$nd$的指数级增长。这种算法加速可由Ising机等专用硬件加速器补充，后者通过大规模并行、流水线及无时钟混合信号操作（通过电路与架构协同设计以匹配算法实现）每秒获取大量样本。我们将任意量子电路映射至带复数能量函数的Boltzmann机的成果，应有助于拓展概率资源模拟量子电路的边界，并与NISQ时代量子计算机进行比较。
英文摘要：
The primary objective of this paper is to present an exact and general procedure for mapping any sequence of quantum gates onto a network of probabilistic p-bits which can take on one of two values 0 and 1. The first $n$ p-bits represent the input qubits, while the other p-bits represent the qubits after the application of successive gating operations. We can view this structure as a Boltzmann machine whose states each represent a Feynman path leading from an initial configuration of qubits to a final configuration. Each such path has a complex amplitude $ψ$ which can be associated with a complex energy. The real part of this energy can be used to generate samples of Feynman paths in the usual way, while the imaginary part is accounted for by treating the samples as complex entities, unlike ordinary Boltzmann machines where samples are positive. Quantum gates often have purely imaginary energy functions for which all configurations have the same probability and one cannot take advantage of sampling techniques. However, if we can use suitable transformations to introduce a real part in the energy function then powerful sampling algorithms like Gibbs sampling can be harnessed to get acceptable results with far fewer samples and perhaps even escape the exponential scaling with $nd$. This algorithmic acceleration can then be supplemented with special-purpose hardware accelerators like Ising Machines which can obtain a very large number of samples per second through a combination of massive parallelism, pipelining, and clockless mixed-signal operation made possible by codesigning circuits and architectures to match the algorithm. Our results for mapping an arbitrary quantum circuit to a Boltzmann machine with a complex energy function should help push the boundaries of the simulability of quantum circuits with probabilistic resources and compare them with NISQ-era quantum computers.
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。
