Quantum complexity phase transitions in monitored random circuits

Understand

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.

• The latter refers to a sudden change in a property of a state of $n$ qubits, such as its entanglement entropy, depending on the rate at which individual qubits are measured.
• At the same time, quantum complexity emerged as a key quantity for the identification of complex behaviour in quantum many-body dynamics.
• 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.