Extending the Variational Quantum Eigensolver to Finite Temperatures

Abstract

We present a variational quantum thermalizer (VQT), called quantum-VQT (qVQT), which extends the variational quantum eigensolver (VQE) to finite temperatures. The qVQT makes use of an intermediate measurement between two variational circuits to encode a density matrix on a quantum device. A classical optimization provides the thermal state and, simultaneously, all associated excited states of a quantum mechanical system. We demonstrate the capabilities of the qVQT for two different spin systems. First, we analyze the performance of qVQT as a function of the circuit depth and the temperature for a 1-dimensional Heisenberg chain. Second, we use the excited states to map the complete, temperature dependent phase diagram of a 2-dimensional J1-J2 Heisenberg model. The numerical experiments demonstrate the efficiency of our approach, which can be readily applied to study various quantum many-body systems at finite temperatures on currently available NISQ devices.

10 pages, 7 figures

References in corpus (8)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Strong quantum computational advantage using a superconducting quantum processor
• The Variational Quantum Eigensolver: a review of methods and best practices
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Scalable mitigation of measurement errors on quantum computers
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm
• Thermal variational quantum simulation on a superconducting quantum processor

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• Variational quantum computing for quantum simulation: principles, implementations, and challenges
• State preparation of lattice field theories using quantum optimal control
• Quantum computation in fermionic thermal field theories
• Estimating molecular thermal averages with the quantum equation of motion and informationally complete measurements
• Exploring thermal equilibria of the Fermi-Hubbard model with variational quantum algorithms
• Thermal state preparation by repeated interactions at and beyond the Lindblad limit