MADs define a hierarchy of distinguishability measures for multi-time quantum processes that increases with coherent memory dimension and saturates the strategy-norm benchmark at finite memory.
Process Tensor Approaches to Non-Markovian Quantum Dynamics
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The paradigm of considering open quantum systems -- i.e. focusing only on the system of interest, and treating the rest of the world as an effective environment -- has proven to be a highly effective way to understand a range of quantum systems, across areas of study such as quantum optics, cold atoms, superconducting qubits, and impurities in solid-state systems. A common approach in many of these contexts has been to consider simplified approaches based on the Born and Markov approximations. While these approximations are indeed often appropriate in contexts such as quantum optics, the widespread application of these approximations has been driven more by simplicity than by accuracy. In particular, these Markovian treatments will fail in many cases, such as when coupling to the environment is not weak, when the environment is structured and has resonances, when the system couples to low-frequency modes of the environment, or when the questions of interest involve the propagation of information through the environment. Despite the fact that many real problems are non-Markovian, the Markov approximation is still widely used, as it is often assumed that a fully non-Markovian treatment is too complex to be practical. In this perspective we discuss a recently developed set of techniques that address this challenge. Centering our discussion around the notion of the process tensor, we demonstrate that the generality of the process tensor concept, coupled with efficient tensor-network methods, opens the door to the description of a wide range of observable non-Markovian processes in a wide range of open quantum systems.
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A new algorithm converts low-entanglement bosonic Gaussian states to matrix product states in polynomial time without hafnian calculations, yielding speedups on experimental boson sampling data.
A periodic matrix product operator representation of the influence functional yields a numerically exact Floquet propagator for non-Markovian dynamics in strongly damped driven quantum systems.
In the monitored symmetric exclusion process, the local Markovianization timescale tracks the global-charge learnability timescale and diverges in the charge-fuzzy phase.
Generic ergodic Hamiltonian dynamics in quantum Ising chains exhibits a long mesoscopic regime in temporal entanglement that deviates from random-circuit universality, suggesting slow spectral reorganization of the influence functional.
Systematic numerical benchmarking shows Floquet master equation accuracy tracks their underlying assumptions, with secular-approximation versions failing near resonances while non-secular versions show smoother error dependence on drive parameters.
Introductory lecture notes on tensor networks with emphasis on matrix-product states, their algorithms, higher-dimensional generalizations, and applications to mixed states and open quantum systems, accompanied by Julia code.
citing papers explorer
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Distinguishing quantum processes with bounded coherent memory
MADs define a hierarchy of distinguishability measures for multi-time quantum processes that increases with coherent memory dimension and saturates the strategy-norm benchmark at finite memory.
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Efficient simulation of low-entanglement bosonic Gaussian states in polynomial time
A new algorithm converts low-entanglement bosonic Gaussian states to matrix product states in polynomial time without hafnian calculations, yielding speedups on experimental boson sampling data.
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Exact Floquet dynamics of strongly damped driven quantum systems
A periodic matrix product operator representation of the influence functional yields a numerically exact Floquet propagator for non-Markovian dynamics in strongly damped driven quantum systems.
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Local Markov Order and Global Inference in Many-Body Dynamics
In the monitored symmetric exclusion process, the local Markovianization timescale tracks the global-charge learnability timescale and diverges in the charge-fuzzy phase.
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Mesoscopic Regimes of Temporal Entanglement in Ergodic Quantum Systems
Generic ergodic Hamiltonian dynamics in quantum Ising chains exhibits a long mesoscopic regime in temporal entanglement that deviates from random-circuit universality, suggesting slow spectral reorganization of the influence functional.
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Benchmarking Floquet Master Equations for Periodically Driven Open Quantum Systems
Systematic numerical benchmarking shows Floquet master equation accuracy tracks their underlying assumptions, with secular-approximation versions failing near resonances while non-secular versions show smoother error dependence on drive parameters.
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Introduction to matrix-product states and tensor networks
Introductory lecture notes on tensor networks with emphasis on matrix-product states, their algorithms, higher-dimensional generalizations, and applications to mixed states and open quantum systems, accompanied by Julia code.