Scalable quantum algorithms for the simulation of quantum many-body systems
in thermal equilibrium are important for predicting properties of quantum
matter at finite temperatures. Here we describe and benchmark a quantum
computing version of the minimally entangled typical thermal states (METTS)
algorithm for which we adopt an adaptive variational approach to perform the
required quantum imaginary time evolution. The algorithm, which we name
AVQMETTS, dynamically generates compact and problem-specific quantum circuits,
which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We
benchmark AVQMETTS on statevector simulators and perform thermal energy
calculations of integrable and nonintegrable quantum spin models in one and two
dimensions and demonstrate an approximately linear system-size scaling of the
circuit complexity. We further map out the finite-temperature phase transition
line of the two-dimensional transverse field Ising model. Finally, we study the
impact of noise on AVQMETTS calculations using a phenomenological noise model.Comment: 13 pages, 6 figure