Exact Model Reduction for Continuous-Time Open Quantum Dynamics

TL;DR

This paper introduces a systematic method for exactly reducing the complexity of continuous-time open quantum systems, enabling efficient simulation while preserving essential dynamics and structural properties.

Contribution

The authors develop a novel reduction technique using Krylov operator spaces that produces minimal-dimensional models, maintaining physical constraints and extending symmetry-based methods.

Findings

Successfully reduces models for open quantum systems with exact dynamics

Preserves Lindblad form in reduced quantum generators

Demonstrates effectiveness on systems like spin chains and quantum codes

Abstract

We consider finite-dimensional many-body quantum systems described by time-independent Hamiltonians and Markovian master equations, and present a systematic method for constructing smaller-dimensional, reduced models that exactly reproduce the time evolution of a set of initial conditions or observables of interest. Our approach exploits Krylov operator spaces and their extension to operator algebras, and may be used to obtain reduced linear models of minimal dimension, well-suited for simulation on classical computers, or reduced quantum models that preserve the structural constraints of physically admissible quantum dynamics, as required for simulation on quantum computers. Notably, we prove that the reduced quantum-dynamical generator is still in Lindblad form. By introducing a new type of observable-dependent symmetries, we show that our method provides a non-trivial generalization of techniques that leverage symmetries, unlocking new reduction opportunities. We quantitatively benchmark our method on paradigmatic open many-body systems of relevance to condensed-matter and quantum-information physics. In particular, we demonstrate how our reduced models can quantitatively describe decoherence dynamics in central-spin systems coupled to structured environments, magnetization transport in boundary-driven dissipative spin chains, and unwanted error dynamics on information encoded in a noiseless quantum code.