Digital Heater: Engineering Thermal Distributions on Quantum Computers

Dynamically generating thermal states of quantum systems is difficult, and requires modeling a macroscopic environment or obtaining detailed knowledge of the system energy spectra. Modeling the macroscopic environment on a quantum simulator may be achieved by coupling ancillary qubits such that each of the transitions in the system spectrum is covered. This approach requires an exponential number of ancillary degrees of freedom which is impractical. We develop a quantum algorithm that uses spectral combing with ancillary qubits that are on average in a thermal state. Our algorithm simulates a large bath while only requiring linear complexity by periodically modulating the ancilla energy over a time period. We evaluate the algorithm by determining error in magnetization of the finite-temperature transverse Ising model.