Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware

TL;DR

This study demonstrates how repeated measurements on a quantum processor induce partial or full thermalization, depending on the commutation relations between the Hamiltonian and measurement observable, with implications for quantum state control.

Contribution

It provides experimental evidence of measurement-induced thermalization and characterizes the conditions leading to partial or infinite-temperature states on quantum hardware.

Findings

Non-commuting Hamiltonian and observable lead to infinite-temperature thermalization.

Commuting operators result in block-diagonal states with finite effective temperature.

Hardware noise modeled as depolarizing channels affects the observed thermalization behavior.

Abstract

On a quantum superconducting processor we observe partial and infinite-temperature thermalization induced by a sequence of repeated quantum projective measurements, interspersed by a unitary (Hamiltonian) evolution. Specifically, on a qubit and two-qubit systems, we test the state convergence of a monitored quantum system in the limit of a large number of quantum measurements, depending on the non-commutativity of the Hamiltonian and the measurement observable. When the Hamiltonian and observable do not commute, the convergence is uniform towards the infinite-temperature state. Conversely, whenever the two operators have one or more eigenvectors in common in their spectral decomposition, the state of the monitored system converges differently in the subspaces spanned by the measurement observable eigenstates. As a result, we show that the convergence does not tend to a completely mixed (infinite-temperature) state, but to a block-diagonal state in the observable basis, with a finite effective temperature in each measurement subspace. Finally, we quantify the effects of the quantum hardware noise on the data by modelling them by means of depolarizing quantum channels.