Effective dynamics of qubit networks via phase-covariant quantum ensembles

TL;DR

This paper introduces a method to efficiently generate ensembles of phase-covariant quantum dynamical maps for spins in closed quantum systems, enabling the study of complex many-body dynamics and noise effects.

Contribution

The authors develop a constructive procedure to produce ensembles of dynamical maps with controlled properties, including disordered and noisy Hamiltonian realizations, from small system dynamics.

Findings

Derived a method to generate ensembles of phase-covariant maps.

Established a procedure to extract time-homogeneous dynamics via averaging.

Demonstrated the ability to model disordered and noisy Hamiltonian ensembles.

Abstract

We derive a new constructive procedure to rapidly generate ensembles of phase-covariant dynamical maps that may be associated to the individual spins of a closed quantum system. We do this by first computing the single-spin dynamical maps in small XXZ networks and chains, specialized to the class of initial states that guarantees phase-covariant dynamics for each spin. Since the dynamics in any small, closed system contains oscillatory features associated to the system size, we define an averaging procedure to extract time-homogeneous dynamics. We use the the average map and the set of deviations from the average map in the exactly derived ensembles to motivate the form of distributional functions for map parameters. The distributions then straightforwardly generate arbitrary-sized ensembles of channels, constrained by a few global properties. This procedure can also generate ensembles where individual maps are not phase-covariant although the average map is, corresponding to realizations of disordered, or noisy, Hamiltonians. The construction procedure suggests new ways to realize random families of open-system dynamics, subject to constraints that require the ensemble to approximate a partition of a closed system.