Abstract
Many simulation tasks require that one first prepare a system's Gibbs state.
We present a family of quantum circuits for variational preparation of thermal
Gibbs states on a quantum computer; we call them the thermal multi-scale
entanglement renormalization ansatz (TMERA). TMERA circuits transform input
qubits to wavepacket modes localized to varying length scales and approximate a
systems Gibbs state as a mixed state of these modes. The TMERA is a based on
the deep multi-scale entanglement renormalization ansatz (DMERA); a TMERA
modifies a ground-state DMERA circuit by preparing each input qubit as a mixed
state. The excitation probabilities for input qubits serve as variational
parameters used to target particular temperature Gibbs states. Since a TMERA is
a special case of the product spectrum ansatz for thermal states, it is simple
to prepare, analyze, and optimize. We benchmark the TMERA on the transverse
field Ising model in one dimension and find that for $D=6$ it produces global
fidelities $\mathcal F > 0.4$ for 512-site systems across all temperatures.