A discrete memory-kernel for multi-time correlations in non-Markovian quantum processes

Abstract

Efficient simulations of the dynamics of open systems is of wide importance for quantum science and tech-nology. Here, we introduce a generalization of the transfer-tensor, or discrete-time memory kernel, formalism to multi-time measurement scenarios. The transfer-tensor method sets out to compute the state of an open few-body quantum system at long times, given that only short-time system trajectories are available. Here, we showthat the transfer-tensor method can be extended to processes which include multiple interrogations (e.g. measurements) of the open system dynamics as it evolves, allowing us to propagate high order short-time correlation functions to later times, without further recourse to the underlying system-environment evolution. Our approach exploits the process-tensor description of open quantum processes to represent and propagate the dynamics in terms of an object from which any multi-time correlation can be extracted. As an illustration of the utility of the method, we study the build-up of system-environment correlations in the paradigmatic spin-boson model, and compute steady-state emission spectra, taking fully into account system-environment correlations present in the steady state.

arXiv comment9 pages, 2 figures

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• Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra
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• Capturing long-range memory structures with tree-geometry process tensors
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• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Hidden Quantum Memory: Is Memory There When Somebody Looks?
• Unifying methods for optimal control in non-Markovian quantum systems via process tensors
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