通过弗洛凯诱导矩阵模型对动态时空上的规范理论进行量子模拟
Quantum simulation of gauge theories on dynamical spacetimes via Floquet-induced matrix models
AI总结：
该研究利用弗洛凯框架使大N矩阵模型可用于可编程量子平台，通过矩阵算子周期性序列演化的哈尔随机态保真度再现杨-米尔斯矩阵模型的欧几里得路径积分权重，贡献是开辟新量子模拟方法。
摘要：
规范理论的量子模拟通常基于空间晶格，大N矩阵模型提供了一种替代方案。本文引入弗洛凯框架，使这些模型可直接用于可编程量子平台。通过矩阵算子周期序列演化的哈尔随机态保真度再现杨-米尔斯矩阵模型的欧几里得路径积分权重，避免固定时空晶格，为量子模拟开辟新途径。
英文摘要：
Quantum simulations of gauge theories are typically built on spatial lattices, an approach that has enabled major progress at the cost of requiring fixed background geometries and obscuring the treatment of curved and dynamical spacetimes. Large-$N$ matrix models offer an alternative, encoding spacetime geometry and gauge fields in the commutation structure of a set of Hermitian matrices, with the classical continuum emerging smoothly at large matrix dimensions. Here we introduce a Floquet framework that makes these models directly accessible to programmable quantum platforms. We show that Euclidean path integral weights of a Yang-Mills matrix models are reproduced, at leading order in the coupling, by the ensemble-averaged fidelities of Haar-random states evolved under periodic sequences of matrix operators. The observables for the simulated matrix model can then be accessed through established randomized benchmarking protocols in terms of the Loschmidt echo. The encoding requires exponentially fewer qubits than canonically quantized approaches. Numerically, we validate the fidelity-weight correspondence, demonstrate parallelized quantum circuits that sample the path-integral measure, and identify the deconfinement transition of an $SU(2)$ gauge field on both flat and expanding cosmological backgrounds. By avoiding a fixed spacetime lattice, the framework preserves continuous symmetries and unitarity on dynamical geometries, opening quantum simulation to field and spacetime dynamics beyond the reach of conventional lattice methods.
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