The Measurement-induced Transition in Long-range Interacting Quantum Circuits

TL;DR

This paper investigates how long-range interactions in quantum circuits affect measurement-induced phase transitions, revealing a shift from conformal to non-conformal universality classes with varying critical exponents.

Contribution

It demonstrates that long-range interactions fundamentally change the universality class of measurement-induced transitions, introducing a continuum of non-conformal classes and providing a phase diagram and theoretical understanding.

Findings

Transition is conformal for weak power-laws

Beyond a critical power-law, non-conformal universality classes emerge

Phase diagram mapped as a function of power-law exponent and measurement rate

Abstract

The competition between scrambling unitary evolution and projective measurements leads to a phase transition in the dynamics of quantum entanglement. Here, we demonstrate that the nature of this transition is fundamentally altered by the presence of long-range, power-law interactions. For sufficiently weak power-laws, the measurement-induced transition is described by conformal field theory, analogous to short-range-interacting hybrid circuits. However, beyond a critical power-law, we demonstrate that long-range interactions give rise to a continuum of non-conformal universality classes, with continuously varying critical exponents. We numerically determine the phase diagram for a one-dimensional, long-range-interacting hybrid circuit model as a function of the power-law exponent and the measurement rate. Finally, by using an analytic mapping to a long-range quantum Ising model, we provide a theoretical understanding for the critical power-law.