Locally suppressed transverse-field protocol for diabatic quantum annealing

Abstract

Diabatic quantum annealing (DQA) is an alternative algorithm to adiabatic quantum annealing that can be used to circumvent the exponential slowdown caused by small minima in the annealing energy spectrum. We present the locally suppressed transverse-field (LSTF) protocol, a heuristic method for making stoquastic optimization problems compatible with DQA. We show that, provided an optimization problem intrinsically has magnetic frustration due to inhomogeneous local fields, a target qubit in the problem can always be manipulated to create a double minimum in the energy gap between the ground and first excited states during the evolution of the algorithm. Such a double energy minimum can be exploited to induce diabatic transitions to the first excited state and back to the ground state. In addition to its relevance to classical and quantum algorithmic speedups, the LSTF protocol enables DQA proof-of-principle and physics experiments to be performed on existing hardware, provided independent controls exist for the transverse qubit magnetization fields. We discuss the implications on the coherence requirements of the quantum annealing hardware when using the LSTF protocol, considering specifically the cases of relaxation and dephasing. We show that the relaxation rate of a large system can be made to depend only on the target qubit, presenting opportunities for the characterization of the decohering environment in a quantum annealing processor.

Effects of XX-catalysts on quantum annealing spectra with perturbative crossings

“…As such, new avenues are being explored for circumventing the computation time scaling problem associated with adiabatic evolution by changing the path the anneal takes from the driver to the problem Hamiltonian. These new methods typically focus on the inhomogeneous driving of the transverse field [13][14][15][16][17][18][19] or the introduction of an additional term to the Hamiltonian referred to as a catalyst [9,16,[20][21][22][23][24][25][26][27]. In general, the goal is to enhance the size of the minimum gap in the annealing spectrum [9, 13-16, 18, 20, 22-24, 27].…”

“…In general, the goal is to enhance the size of the minimum gap in the annealing spectrum [9, 13-16, 18, 20, 22-24, 27]. However, a faster time to solution can also be obtained by manipulating the spectrum such that a diabatic anneal is possible [17,22,25]. In this case the goal is to produce a path through the annealing energy spectrum that exploits transitions to higher energy states such that the system subsequently returns to the ground state.…”