Characterization and thermometry of dissapatively stabilized steady states

TL;DR

This paper investigates dissipatively stabilized steady states in noisy quantum algorithms, demonstrating they can often be approximated as thermal states and proposing methods for effective temperature estimation, with practical implications for near-term quantum hardware.

Contribution

It introduces a method to characterize and thermometrically analyze steady states in dissipatively stabilized quantum algorithms, especially the RQE, using resource-efficient techniques.

Findings

Steady states are often well-approximated by thermal distributions.

Cooling resources can be used effectively for thermometry.

Methods are feasible for implementation on near-term quantum devices.

Abstract

In this work we study the properties of dissipatively stabilized steady states of noisy quantum algorithms, exploring the extent to which they can be well approximated as thermal distributions, and proposing methods to extract the effective temperature T. We study an algorithm called the Relaxational Quantum Eigensolver (RQE), which is one of a family of algorithms that attempt to find ground states and balance error in noisy quantum devices. In RQE, we weakly couple a second register of auxiliary "shadow" qubits to the primary system in Trotterized evolution, thus engineering an approximate zero-temperature bath by periodically resetting the auxiliary qubits during the algorithm's runtime. Balancing the infinite temperature bath of random gate error, RQE returns states with an average energy equal to a constant fraction of the ground state. We probe the steady states of this algorithm for a range of base error rates, using several methods for estimating both T and deviations from thermal behavior. In particular, we both confirm that the steady states of these systems are often well-approximated by thermal distributions, and show that the same resources used for cooling can be adopted for thermometry, yielding a fairly reliable measure of the temperature. These methods could be readily implemented in near-term quantum hardware, and for stabilizing and probing Hamiltonians where simulating approximate thermal states is hard for classical computers.