Nonuniversal Entanglement Level Statistics in Projection-driven Quantum Circuits [article]

Lei Zhang, Justin A. Reyes, Stefanos Kourtis, Claudio Chamon, Eduardo R. Mucciolo, Andrei E. Ruckenstein
2020 arXiv   pre-print
We study the level-spacing statistics in the entanglement spectrum of output states of random universal quantum circuits where qubits are subject to a finite probability of projection to the computational basis at each time step. We encounter two phase transitions with increasing projection rate: The first is the volume-to-area law transition observed in quantum circuits with projective measurements; The second separates the pure Poisson level statistics phase at large projective measurement
more » ... es from a regime of residual level repulsion in the entanglement spectrum within the area-law phase, characterized by non-universal level spacing statistics that interpolates between the Wigner-Dyson and Poisson distributions. By applying a tensor network contraction algorithm introduced in Ref. [1] to the circuit spacetime, we identify this second projective-measurement-driven transition as a percolation transition of entangled bonds. The same behavior is observed in both circuits of random two-qubit unitaries and circuits of universal gate sets, including the set implemented by Google in its Sycamore circuits.
arXiv:2001.11428v1 fatcat:ne3pgzhicjbaxilfaaidhmoosa