Born-rule statistical dynamical quantum phase transitions under measurement

TL;DR

This paper introduces a statistical framework for dynamical quantum phase transitions (DQPTs) based on measurement outcomes, linking them to a statistical model and exploring their properties through analytic continuation and experimental simulation.

Contribution

It develops a novel statistical characterization of DQPTs considering all measurement outcomes, connecting them to a statistical model and proposing an experimental simulation protocol.

Findings

Recovery of DQPT under high-moment averaging

Delocalized level distribution at critical times

Vanishing Yang-Lee-Fisher zeros and level crossing near critical times

Abstract

Dynamical quantum phase transitions (DQPTs) occur at times when a quantum state exhibits a nonanalytic change in its return probability. This can be viewed as the probability of collapsing the evolved state to the initial state by quantum measurement. However, the initial wave function usually has exponentially small amplitude in the late time evolved state. Here we perform statistical characterization for all the possible post-measurement states distributed according to the Born's rule, by sampling a one-dimensional quantum Ising chain after a quantum quench dynamics. The statistical ensemble can also be viewed as a mixed state when the time evolved state is subjected to maximally dephasing noise in a certain basis. We map the distribution to a statistical model and characterize its effective "energy" spectrum, and introduce the average dynamical free energy, establishing a framework for the statistical DQPTs. We show the recovering of DQPT under high-moment average and a delocalized level distribution following critical times. Through analytic continuation into the complex time plane, we demonstrate the vanishing of Yang-Lee-Fisher zeros and the emergent level crossing near critical times. Finally, we propose a measurement-based quantum computation protocol to simulate the unitary evolution via single-qubit measurements on a two-dimensional cluster state. Our results provide a way for experimentally investigating statistical DQPTs in quantum devices, shedding light on the structured circuit sampling with insights from DQPT and generalizing the understanding of mixed state due to decoherence beyond equilibrium.