Digital dissipative state preparation for frustration-free gapless quantum systems

TL;DR

This paper presents a digital protocol using local measurements and feedback to efficiently prepare gapless quantum ground states, revealing universal critical properties and outperforming traditional adiabatic methods.

Contribution

It introduces a novel digital state preparation method for frustration-free gapless systems that scales polynomially and generalizes to many-body quantum states.

Findings

Protocol prepares ground states in polynomial time.

Transient cooling reveals universal critical properties.

Numerical simulations confirm theoretical predictions.

Abstract

Preparing algebraically correlated ground states of quantum many-body systems is an important, yet challenging task for quantum simulation. We introduce a protocol that employs local projective measurements and unitary feedback for frustration-free gapless systems. Our approach prepares a priori unknown ground states in time that scales polynomially with system size. We analytically show the performance our protocol for the dynamics of a single-particle; we argue the same mechanism generalizes to many-body systems based on the physics of quasiparticles. Our theory predicts that a transient cooling dynamics directly reveals the system's universal critical properties. In particular, the state preparation time is linear in the inverse of the finite-size gap (up to log correction) when the system's dynamical critical exponent is larger or equal the effective spatial dimension explored by the quasiparticles. We verify these predictions in numerical simulations of ferromagnetic Heisenberg models in one- and two dimensions, a Fredkin spin chain, and a two-dimensional model of resonating valence bond states. Our protocol stabilizes gapless many-body ground states fully digitally without requiring analog rotations, enabling access to high-fidelity states beyond conventional adiabatic approaches in near-term experiments.