Entanglement Phase Transition with Spin Glass Criticality

We define an ensemble of random Clifford quantum circuits whose output state undergoes an entanglement phase transition between two volume-law phases as a function of measurement rate. Our setup provides an exact map between the entanglement entropy of the quantum state and the ground-state entropy of a spin glass model. We identify the entanglement phases using an order parameter that is accessible on a quantum chip. We extract the critical exponents, which reveal spin glass criticality. Our work establishes an exact statistical mechanics theory of an entanglement phase transition.