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

T. Dörstel1,2, T. Iadecola3,4,5, J. H. Wilson6,7, and M. Buchhold1,2

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Phys. Rev. Lett. 136, 120603 – Published 25 March, 2026

DOI: https://doi.org/10.1103/zp25-ppgk

Abstract

We introduce frustration-free control, a measurement-feedback framework for quantum state preparation that extends frustration-free Hamiltonians to monitored 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 postselection. 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 run-time scaling t∼Lz with transport exponent z=2. Simulations of Motzkin and Fredkin chains reveal subdiffusive scaling z≥83, confirming absorbing-state transport as a general organizing principle for deterministic entangled-state preparation and transport diagnostics in monitored quantum dynamics.

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Phys. Rev. Lett. 136, 120603– Published 25 March, 2026
  • Received 13 November 2025
  • Revised 3 February 2026
  • Accepted 27 February 2026
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