Programmable adiabatic demagnetization for systems with trivial and topological excitations

Preparing the ground state of a many-body Hamiltonian on a quantum device is of central importance, both for quantum simulations of molecules and materials, and for a variety of quantum information task. We propose a simple, robust protocol to prepare a low-energy state of an arbitrary Hamiltonian on a quantum computer. The protocol is inspired by the “adiabatic demagnetization” technique, used to cool solid state systems to extremely low temperatures. The adiabatic cooling protocol is demonstrated via an application to the transverse field Ising model. We use half of the qubits to model the system and the other half as a bath. Each bath spin is coupled to a system spin. In a strong magnetic field, the bath spins are prepared in the polarized ground state. By an adiabatic downward sweep of the magnetic field, we change the energy of the bath spins and allow for resonant processes that transfer entropy from the system to the bath qubits. After each cycle, the bath is reset to the ground state.

We find that the performance of the algorithm in the presence of a finite error rate depends on the nature of the excitations of the system; systems with non-local (topological) excitations are more difficult to cool. Finally, we explore ways to partially mitigate this problem.