Designing open quantum systems with known steady states: Davies generators and beyond

Guo, Jinkang; Hart, Oliver; Chen, Chi-Fang; Friedman, Aaron J.; Lucas, Andrew

doi:10.22331/q-2025-01-28-1612

Title: Designing open quantum systems with known steady states: Davies generators and beyond

Journal Article · 28 January 2025 · Quantum

DOI: https://doi.org/10.22331/q-2025-01-28-1612 · OSTI ID:2507247

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Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA
Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, 91125 USA

We provide a systematic framework for constructing generic models of nonequilibrium quantum dynamics with a target stationary (mixed) state. Our framework identifies (almost) all combinations of Hamiltonian and dissipative dynamics that relax to a steady state of interest, generalizing the Davies’ generator for dissipative relaxation at finite temperature to nonequilibrium dynamics targeting arbitrary stationary states. We focus on Gibbs states of stabilizer Hamiltonians, identifying local Lindbladians compatible therewith by constraining the rates of dissipative and unitary processes. Moreover, given terms in the Lindbladian not compatible with the target state, our formalism identifies the operations – including syndrome measurements and local feedback – one must apply to correct these errors. Our methods also reveal new models of quantum dynamics: for example, we provide a “measurement-induced phase transition” in which measurable two-point functions exhibit critical (power-law) scaling with distance at a critical ratio of the transverse field and rate of measurement and feedback. Time-reversal symmetry – defined naturally within our formalism – can be broken both in effectively classical and intrinsically quantum ways. Our framework provides a systematic starting point for exploring the landscape of dynamical universality classes in open quantum systems, as well as identifying new protocols for quantum error correction.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0024324

OSTI ID:: 2507247

Journal Information:: Quantum, Journal Name: Quantum Vol. 9; ISSN 2521-327X

Publisher:: Verein zur Forderung des Open Access Publizierens in den QuantenwissenschaftenCopyright Statement

Country of Publication:: Austria

Language:: English

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