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

TL;DR

This paper develops a comprehensive framework for designing open quantum systems with predetermined steady states, extending Davies' generator to nonequilibrium scenarios and uncovering new models including measurement-induced phase transitions.

Contribution

It introduces a systematic method to construct and analyze nonequilibrium quantum dynamics targeting specific stationary states, generalizing existing models and identifying new dynamical phases.

Findings

Identification of local Lindbladians compatible with Gibbs states of stabilizer Hamiltonians

Discovery of a measurement-induced phase transition with critical scaling

Framework for error correction protocols in quantum systems

Abstract

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.