Exact Hidden Markovian Dynamics in Quantum Circuits

TL;DR

This paper introduces a method to construct quantum circuits with exact hidden Markovian dynamics, enabling precise calculation of local observables in complex quantum many-body systems.

Contribution

The authors develop a framework for designing nonintegrable quantum circuits that exhibit exactly solvable hidden Markovian subsystem dynamics, a novel approach in quantum dynamics.

Findings

Exact hidden Markovian property achieved in specific quantum circuits.

Analytical description of subsystem influence via quantum channels.

Concrete examples demonstrating the approach with different local dimensions.

Abstract

Characterizing nonequilibrium dynamics in quantum many-body systems is a challenging frontier of physics. In this Letter, we systematically construct solvable nonintegrable quantum circuits that exhibit exact hidden Markovian subsystem dynamics. This feature thus enables accurately calculating local observables for arbitrary evolution time. Utilizing the influence matrix method, we show that the influence of the time-evolved global system on a finite subsystem can be analytically described by sequential, time-local quantum channels acting on the subsystem with an ancilla of finite Hilbert space dimension. The realization of exact hidden Markovian property is facilitated by a solvable condition on the underlying two-site gates in the quantum circuit. We further present several concrete examples with varying local Hilbert space dimensions to demonstrate our approach.