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Bulletin of the American Physical Society

Tensorial tools for quantum computing

Yannick Meurice

Published Mar 6, 2019• 0 citations
OpenAlex

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In most lattice simulations, the variables of integration are compact and character expansion (for instance Fourier analysis for U(1) models) can be used to rewrite the partition function and average observables as discrete sums of contracted tensors. These reformulations have been used for RG blocking but they also naturally fit the needs of quantum computing. We discuss FAQ about tensorial reformulations: effects of truncations on symmetries, boundary conditions, Grassmann variables, and other recent aspects of quantum computing in the same context.
The generalized quantum master equation provides a powerful framework for non-Markovian dynamics of open quantum systems. However, the accurate and efficient evaluation of the memory kernel remains a challenge. In this work, we introduce a comprehensive tensorial extension to the Memory Kernel Coupling Theory (MKCT) to overcome this bottleneck. By elevating the original scalar formalism to a tensorial framework, the extended MKCT enables the calculation of general expectation values and cross-correlation functions. We demonstrate the numerical accuracy and efficiency of this method across multiple benchmark systems: capturing transient populations and coherences in the spin-boson model, resolving the excitonic absorption spectrum of the Fenna-Matthews-Olson complex, and simulating charge mobility in one-dimensional lattice models. These successful applications establish the tensorial MKCT as a highly efficient tool for investigating complex dynamics in open quantum systems.