Generalized hydrodynamics of integrable quantum circuits

TL;DR

This paper develops an exact large-scale description of integrable quantum circuits using generalized hydrodynamics, revealing how discrete Trotter steps can qualitatively alter nonequilibrium dynamics compared to continuous evolution.

Contribution

It introduces a novel application of generalized hydrodynamics to integrable quantum circuits, capturing the effects of finite Trotter steps on large-scale dynamics.

Findings

Discrete Trotter steps can qualitatively change the dynamics.

A single defect at the junction can alter the late-time macrostate.

The approach predicts different phases depending on parameters.

Abstract

Quantum circuits make it possible to simulate the continuous-time dynamics of a many-body Hamiltonian by implementing discrete Trotter steps of duration $\tau$. However, when $\tau$ is sufficiently large, the discrete dynamics exhibit qualitative differences compared to the original evolution, potentially displaying novel features and many-body effects. We study an interesting example of this phenomenon, by considering the integrable Trotterization of a prototypical integrable model, the XXZ Heisenberg spin chain. We focus on the well-known bipartition protocol, where two halves of a large system are prepared in different macrostates and suddenly joined together, yielding non-trivial nonequilibrium dynamics. Building upon recent results and adapting the generalized hydrodynamics (GHD) of integrable models, we develop an exact large-scale description of an explicit one-dimensional quantum-circuit setting, where the input left and right qubits are initialized in two distinct product states. We explore the phenomenology predicted by the GHD equations, which depend on the Trotter step and the gate parameters. In some phases of the parameter space, we show that the quantum-circuit large-scale dynamics is qualitatively different compared to the continuous-time evolution. In particular, we find that a single microscopic defect at the junction, such as the addition of a single qubit, may change the nonequilibrium macrostate appearing at late time.