Simulation of Measurement-Induced Entanglement Entropy Transitions

Sammanfattning

Measurement-induced entanglement transitions arise in quantum circuits of unitary gates and measurements, referred to as hybrid circuits. On average, unitary dynamics generate entanglement, and measurements suppress entanglement. In one-dimensional hybrid circuits, this competition leads to a transition between an area-law phase when the probability of measurements is higher, and a volume-law entangled phase when the probability is lower. In this thesis, the phase transition is studied using two different approaches. First, state vector simulations are performed for hybrid circuits composed of Haar-random unitary gates and random Clifford gates. This allows for direct access to the state vectors and entanglement entropy, but is only feasible for smaller size systems (up to 12 qubits). Second, a traffic flow model is implemented as an approximation to stabiliser dynamics of Clifford circuits, which is studied for larger systems (up to 2048 qubits). Scaling analyses are carried out for both approaches to investigate the dependence of the steady-state entropy on system size and measurement probability. Data collapses of simulation data for different circuit sizes are obtained using both a logarithmic form S−αlnN and by also including an additional correction S−αlnN+βN^(−ω) where ω = 1, leading to a more accurate collapse for smaller sizes. Both the state vector model and traffic flow model lead to a phase transition in entanglement entropy, but with different critical parameters. This indicates that the traffic flow model and the quantum circuit models do not belong to the same universality class. The results clarify the efficiency but also limitations of classical models for describing measurement-induced entanglement transitions.