Improving Quantum Annealing through microcanonical thermalization: a one-dimensional study*

Random-Field Quantum Annealing (RFQA) is a recently-proposed analog protocol where a quantum system is coherently driven by oscillating an extensive number of single-spin operators at independent low frequencies, with the goal of quickly populating both energy levels involved in an avoided crossing ("microcanonical thermalization") so as to counter the exponential ground-state depletion encountered by standard QA in first-order phase transitions.

In our work we use TEBD methods to simulate the RFQA driver in a one-dimensional Transverse-Field Ising chain. We study tunnelling times between the two quasi-degenerate ferromagnetic ground states by ramping up the transverse field from zero to a finite value Γ, waiting for tunnelling, and then ramping down again. We compare the RFQA results with a reverse-annealing protocol that uses a uniform transverse field. We observe an asymptotic advantage in favour of RFQA in the time-to-solution metric, with a separation that increases as Γ→Γ_c. We discuss how RFQA can be used to ameliorate the effect of minor embedding in QA as well as to provide a possible mechanism for quantum speedup in more realistic combinatorial optimization problems.