Berlin 2024 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 3: Focus Session: Quantum Interactive Dynamics I (joint session DY/TT)
DY 3.5: Vortrag
Montag, 18. März 2024, 11:15–11:30, A 151
Entanglement Transitions in Unitary Circuit Games — •Raúl Morral-Yepes1,2, Adam Smith3, Shivaji L. Sondhi4, and Frank Pollmann1,2 — 1Technical University of Munich, Garching, Germany — 2Munich Center for Quantum Science and Technology (MCQST), München, Germany — 3University of Nottingham, Nottingham, UK — 4University of Oxford, Oxford, UK
Repeated projective measurements in unitary circuits can lead to an entanglement phase transition as the measurement rate is tuned. In this work, we consider a different setting in which the projective measurements are replaced by dynamically chosen unitary gates that minimize the entanglement. This can be seen as a one-dimensional unitary circuit game in which two players get to place unitary gates on randomly assigned bonds at different rates: The “entangler” applies a random local unitary gate with the aim of generating extensive (volume law) entanglement. The “disentangler”, based on limited knowledge about the state, chooses a unitary gate to reduce the entanglement entropy on the assigned bond with the goal of limiting to only finite (area law) entanglement. In order to elucidate the resulting entanglement dynamics, we consider three different scenarios: (i) a classical discrete height model, (ii) a Clifford circuit, and (iii) a general U(4) unitary circuit. We find that both the classical and Clifford circuit models exhibit phase transitions as a function of the rate that the disentangler places a gate. In contrast, the entangler always wins when using Haar random unitary gates and we observe extensive, volume law entanglement for all non-zero rates of entangling.
Keywords: phase transitions; unitary dynamics; entanglement; surface growth; random circuits