Journal
PHYSICAL REVIEW B
Volume 101, Issue 23, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.101.235104
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Funding
- J.A.R
- NSF [CCF-1844190]
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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. We identify a second transition within the area law phase by repartioning the system randomly into two subsystems and probing the entanglement level statistics. This second transition separates a pure Poisson level statistics phase at large projective measurement rates from a regime of residual level repulsion in the entanglement spectrum, characterized by nonuniversal level spacing statistics that interpolates between the Wigner-Dyson and Poisson distributions. By applying a tensor network contraction algorithm introduced in [Z.-C. Yang et al., Phys. Rev. E 97, 033303 (2018)] 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.
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