Frustration-Free Control and Absorbing-State Transport in Entangled State Preparation

TL;DR

This paper introduces a measurement-feedback protocol for quantum state preparation that leverages frustration-free control and emergent charge transport to efficiently generate highly entangled states.

Contribution

It extends frustration-free Hamiltonian concepts to stochastic dynamics, revealing how charge transport governs relaxation in entangled state preparation.

Findings

Relaxation to the target state follows a transport process with a scaling exponent z=2.

Simulations show subdiffusive scaling with z ≥ 8/3 in certain quantum chains.

The protocol enables controlled entangled-state preparation via minimal local corrections.

Abstract

We study frustration-free control, a measurement-feedback protocol for quantum state preparation that extends the concept of frustration-free Hamiltonians to stochastic dynamics. The protocol drives many-body systems into highly entangled target states, common dark states of all measurement projectors, through minimal local unitary corrections that realize an absorbing-state dynamics without post-selection. We show that relaxation to the target state is governed by emergent transport of nonlocal charges, such as singlet excitations in SU$(2)$-symmetric dynamics. While measurement-feedback annihilates compatible charge configurations, both measurement and scrambling unitaries induce charge transport and thus determine the convergence time. Mapping a baseline model of SU$(N)$ SWAP measurements with local corrections to a solvable absorbing random walk yields a runtime scaling $t \sim L^z$ with transport exponent $z=2$. Simulations of Motzkin and Fredkin chains reveal subdiffusive scaling $z \ge \tfrac{8}{3}$, confirming the transport picture and suggesting strategies for controlled entangled-state preparation and charge-transport probing in monitored quantum dynamics.