Mapping quantum circuits onto statistical-mechanical models offers a powerful framework for exploring their collective behavior. Previous work has shown that the disorder-averaged ensemble of a d-dimensional error-mitigated Haar-random circuit can be mapped to a (d+1) dimensional random-field Ising model, which exhibits a phase transition for d≥3d. However, for d≥2, even though the Rényi-2 entropy obeys an area law, the matrix product state (MPS) representation of the averaged density matrix requires a bond dimension that grows exponentially with system size to faithfully capture the critical point — rendering large-scale simulations impractical. We propose a protocol that overcomes this limitation by directly employing a heavily truncated MPS representation, enabling the detection of phase transitions with a constant bond dimension. Numerical simulations demonstrate that, despite substantial truncation errors, the estimated critical point in the all-to-all geometry agrees well with exact results from small-system calculations reported in previous studies. Furthermore, we verify that the protocol is applicable in both 1+1 and 2+1-dimensional settings, providing a scalable and efficient tool for investigating phase transitions in error-mitigated noisy quantum circuits.

Pizza and drinks will be served after the seminar in ATL 2117.