Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits

TL;DR

This paper explores how irreversibility in quantum circuits relates to entanglement and spectral statistics, showing that universal gates lead to Wigner-Dyson level spacing and irreversibility, while non-universal gates do not.

Contribution

It establishes a connection between irreversibility, entanglement spectrum statistics, and universality of quantum gates in quantum circuits.

Findings

Universal gates produce Wigner-Dyson statistics and irreversibility.

Non-universal gates lead to deviations from Wigner-Dyson statistics.

Disentangling algorithms succeed with non-universal gates.

Abstract

We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal gates for quantum computation. If, on the other hand, the system is evolved with a non-universal set of gates, the statistics of the entanglement level spacing deviates from Wigner-Dyson and the disentangling algorithm succeeds. These results open a new way to characterize irreversibility in quantum systems.