Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss

TL;DR

This paper investigates how simultaneous qubit loss and measurement errors in quantum circuits lead to a flow from percolation to Nishimori universality, revealing complex entanglement dynamics and multifractal spectra through extensive simulations.

Contribution

It demonstrates the critical RG flow from percolation to Nishimori universality in weakly monitored quantum circuits with combined errors, extending understanding of entanglement transitions.

Findings

Critical RG flow from percolation to Nishimori universality identified.

Infinitesimal deviations from Clifford regime cause non-monotonic entanglement growth.

Exact multifractal spectrum derived for percolation; high-precision exponents for Nishimori fixed point.

Abstract

In circuit-based quantum state preparation, qubit loss and coherent errors are circuit imperfections that imperil the formation of long-range entanglement beyond a certain threshold. The critical theory at the threshold is a continuous entanglement transition known to be described by a (2+0)-dimensional non-unitary conformal field theory which, for the two types of imperfections of certain circuits, is described by either percolation or Nishimori criticality, respectively. Here we study the threshold behavior when the two types of errors simultaneously occur and show that, when moving away from the Clifford-regime of projective stabilizer measurements, the percolation critical point becomes unstable and the critical theory flows to Nishimori universality. We track this critical renormalization group (RG) crossover flow by mapping out the entanglement phase diagrams, parametrized by the probability and strength of random weak measurements, of two dual protocols preparing surface code or GHZ-class cat states from a parent cluster state via constant-depth circuits. Extensive numerical simulations, using hybrid Gaussian fermion and tensor network / Monte Carlo sampling techniques on systems with more than a million qubits, demonstrate that an infinitesimal deviation from the Clifford regime leads to a sudden, strongly non-monotonic entanglement growth at the incipient non-unitary RG flow. We argue that spectra of scaling dimensions of both the percolation and Nishimori fixed points exhibit multifractality. For percolation, we provide the exact (non-quadratic) multifractal spectrum of exponents, while for the Nishimori fixed point we show high-precision numerical results for five leading exponents characterizing multifractality.