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

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.

A Dyson Brownian Motion Model for Weak Measurements in Chaotic Quantum Systems

“…Recent results have attempted to study this phenomenology in simplified toy models [37,38]. However, in the case of noninteracting systems (e.g., free fermions), it has been shown that the transition has a radically different nature: the volume-law phase is immediately unstable for arbitrarily weak quantum measurements [39][40][41][42][43][44][45], and yet, in some cases, a subvolume phase can survive before the onset of the area-law phase [46][47][48][49][50], with a universality class more akin to problems of Anderson localization and disordered conductors, studied in the context of nonlinear sigma models [51,52]. In the interacting case, one of the main difficulties in studying individual trajectories of monitored systems lies in the fact that the probability of each trajectory depends on the state itself, in accordance with Born's rule.…”

Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain

“…In particular, it has been established that quantum systems subjected to both measurements and unitary dynamics offer another class of dynamical behavior described in terms of quantum trajectories [6], and well explored in the context of quantum circuits [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], quantum spin systems [26][27][28][29][30][31][32][33][34][35][36][37], trapped atoms [38], and trapped ions [39][40][41]. In this context, the bipartite entanglement entropy of isolated systems grows over time and eventually reaches the order of the system size as predicted by the celebrated Cardy-Calabrese quasi-particle picture [42][43][44][45].…”