Disorder-Free Localization for Benchmarking Quantum Computers

TL;DR

This paper demonstrates how disorder-free localization can be implemented on quantum computers to serve as a benchmark for their performance, leveraging emergent local symmetries and entanglement dynamics.

Contribution

It introduces an efficient encoding method for implementing a canonical DFL model on gate-based quantum computers, enabling robust benchmarking.

Findings

Efficient encoding of three-qubit gates for DFL simulation

Observation of absence of correlation spreading as a benchmark

Tunable entanglement growth to volume law for testing quantum capabilities

Abstract

Disorder-free localization (DFL) is a phenomenon as striking as it appears to be simple: a translationally invariant state evolving under a disorder-free Hamiltonian failing to thermalize. It is predicted to occur in a number of quantum systems exhibiting emergent or native \emph{local} symmetries. These include models of lattice gauge theories and, perhaps most simply, some two-component spin chains. Though well-established analytically for special soluble examples, numerical studies of generic systems have proven difficult. Moreover, the required local symmetries are a challenge for any experimental realization. Here, we show how a canonical model of DFL can be efficiently implemented on gate-based quantum computers, which relies on our efficient encoding of three-qubit gates. We show that the simultaneous observation of the absence of correlation spreading and tunable entanglement growth to a volume law provides an ideal testbed for benchmarking the capabilities of quantum computers. In particular, the availability of a soluble limit allows for a rigorous prediction of emergent localization length scales and tunable time scales for the volume law entanglement growth, which are ideal for testing capabilities of scalable quantum computers.