Berlin 2024 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 3: Focus Session: Quantum Interactive Dynamics I (joint session DY/TT)

DY 3.10: Talk

Monday, March 18, 2024, 12:30–12:45, A 151

Quantum complexity phase transitions in monitored random circuits — •Ryotaro Suzuki¹, Jonas Haferkamp², Jens Eisert¹, and Philippe Faist¹ — ¹Freie Universität Berlin — ²Harvard University

Recently, the dynamics of quantum systems that involve both unitary evolution and quantum measurements have attracted attention due to the exotic phenomenon of measurement-induced phase transitions. At the same time, quantum complexity emerged as a key quantity for the identification of complex behaviour in quantum many-body dynamics. Quantum complexity of a quantum state is defined as the minimum number of unitary gates to generate the state by a quantum circuit. In this work, we investigate the dynamics of the quantum state complexity in monitored random circuits, where n qubits evolve according to a random unitary circuit and are individually measured with a fixed probability at each time step. We find that the growth behaviour of the exact quantum state complexity undergoes a phase transition when changing the measurement rate. Below a critical measurement rate, the complexity grows linearly in time until an exponential time in n. Above, the complexity does not grow more than polynomially in n. We lower bound the exact state complexity in the former regime using recently developed techniques based on algebraic geometry.

Keywords: Measurement-induced phase transitions; Quantum complexity; Quantum monitored random circuits; Quantum measurement; Percolation theory