Asymptotically Solvable Quantum Circuits

TL;DR

This paper introduces 'asymptotically solvable' quantum circuits that behave generically at short times but become solvable at long times, providing insights into quantum dynamics and thermalization.

Contribution

The authors define a new class of quantum circuits where solvability emerges only after a certain time scale, bridging the gap between generic and solvable quantum dynamics.

Findings

Circuits are ergodic but contain a non-interacting point.

Exact analytical results for early-time non-solvable regime.

Numerical simulations support the theoretical framework.

Abstract

The discovery of chaotic quantum circuits with (partially) solvable dynamics has played a key role in our understanding of non-equilibrium quantum matter and, at the same time, has helped the development of concrete platforms for quantum computation. It was shown that solvability does not prevent the generation of chaotic dynamics, however, it imposes non-trivial constraints on the generated correlations. A natural question is then whether it is possible to gain insight into the generic case despite the latter being very hard to access. To address this question here we introduce a family of 'asymptotically solvable' quantum circuits where the solvability constraints only affect correlations on length scales beyond a tuneable threshold. This means that their dynamics are only solvable for long enough times: for times shorter than the threshold they are generic. We show this by computing both their dynamical correlations on the equilibrium (infinite temperature) state and their thermalisation dynamics following quantum quenches from compatible (asymptotically solvable) non-equilibrium initial states. The class of systems we introduce is generically ergodic but contains a non-interacting point, which we use to provide exact analytical results, complementing those of numerical experiments, on the non-solvable early time regime.