Variational preparation of finite-temperature states on a quantum computer (Part 1: theory)

Simulating quantum phenomena is one of the most promising applications of Noisy Intermediate Scale Quantum (NISQ) computing systems. In particular, the ability to represent the dynamical evolution of many-body systems has been demonstrated¹. However, the accuracy of these simulations depends on efficient initial state preparation in the quantum computer. Studying temperature-dependent phenomena, like high temperature superconductivity, requires the preparation of thermal equilibrium states called Gibbs states within the NISQ qubit ensembles. Here, we describe a procedure to generate finite-temperature Gibbs states for the transverse-field Ising chain Hamiltonian, via preparation of thermofield double (TFD) states. The TFD states are generated using a hybrid quantum-classical variational algorithm, whose advantages and limitations we discuss.
¹S. Lloyd, Science 273, 1073 (1996).