Entanglement and Absorbing State Transitions in (d+1)-Dimensional Stabilizer Circuits

P. Sieranta, X. Turkeshib, c aICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain bInstitut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany JEIP, USR 3573 CNRS, Collège de France, PSL Research University, 11 Place Marcelin Berthelot, 75321 Paris Cedex 05, France

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We study the influence of feedback operations on the dynamics of (d+1)-dimensional monitored random quantum circuit. Competition between unitary dynamics and measurements leads to an entanglement phase transition, while feedback steers the dynamics towards an absorbing state, yielding an absorbing state phase transition. Based on previous results in one spatial dimension (Phys. Rev. Lett. 130, 120402 (2023)), we discuss the interplay between the two types of transitions for d≥2 in the presence of (i) short-range feedback operations or (ii) additional global control operations. In both cases, the absorbing state transition belongs to the d-dimensional directed percolation universality class. In contrast, the entanglement transition depends on the feedback operation type and reveals dynamics' inequivalent features. The entanglement and absorbing state phase transition remain separated for short-range feedback operations. When global control operations are applied, we find the two critical points coinciding; nevertheless, the universality class may still differ, depending on the choice of control operation.

DOI:10.12693/APhysPolA.144.474 topics: entanglement, monitored quantum dynamics, feedback operations, random circuits