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We present a variational quantum thermalizer (VQT), called quantum-VQT(qVQT), which extends the variational quantum eigensolver (VQE) to finitetemperatures. The qVQT makes use of an intermediate measurement between twovariational circuits to encode a density matrix on a quantum device. Aclassical optimization provides the thermal state and, simultaneously, allassociated excited states of a quantum mechanical system. We demonstrate thecapabilities of the qVQT for two different spin systems. First, we analyze theperformance of qVQT as a function of the circuit depth and the temperature fora 1-dimensional Heisenberg chain. Second, we use the excited states to map thecomplete, temperature dependent phase diagram of a 2-dimensional J1-J2Heisenberg model. The numerical experiments demonstrate the efficiency of ourapproach, which can be readily applied to study various quantum many-bodysystems at finite temperatures on currently available NISQ devices.

Extending the Variational Quantum Eigensolver to Finite Temperatures