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We propose a simple, robust protocol to prepare a low-energy state of anarbitrary Hamiltonian on a quantum computer or programmable quantum simulator.The protocol is inspired by the adiabatic demagnetization technique, used tocool solid-state systems to extremely low temperatures. A fraction of thequbits (or spins) is used to model a spin bath that is coupled to the system.By an adiabatic ramp down of a simulated Zeeman field acting on the bath spins,energy and entropy are extracted from the system. The bath spins are thenmeasured and reset to the polarized state, and the process is repeated untilconvergence to a low-energy steady state is achieved. We demonstrate theprotocol via application to the quantum Ising model. We study the protocol'sperformance in the presence of noise and show how the information from themeasurement of the bath spins can be used to monitor the cooling process. Theperformance of the algorithm depends on the nature of the excitations of thesystem; systems with non-local (topological) excitations are more difficult tocool than those with local excitations. We explore the possible mitigation ofthis problem by trapping topological excitations.

Programmable adiabatic demagnetization for systems with trivial and topological excitations