Preparing quantum many-body scar states on quantum computers

TL;DR

This paper develops quantum algorithms and protocols to prepare and study quantum many-body scar states, enabling exploration of their properties and dynamics on quantum computers, including experimental demonstrations.

Contribution

It introduces novel quantum state preparation methods for scar states, including both exact and variational approaches, and demonstrates their feasibility on real quantum hardware.

Findings

Protocols for preparing individual scar states and superpositions.

Finite-depth nonunitary protocol using measurement and postselection.

Proof-of-principle experiments on superconducting quantum hardware.

Abstract

Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols that enable the use of quantum computers to study this question. We present protocols both for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we present both a system-size-linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we formulate an exact state preparation approach based on matrix product states that yields quasipolynomial-depth circuits, as well as a variational approach with a polynomial-depth ansatz circuit. We also provide proof of principle state-preparation demonstrations on superconducting quantum hardware.