Diabatic quantum annealing for the frustrated ring model

Abstract

Quantum annealing is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare ground state and a problem Hamiltonian whose ground state encodes solutions to an optimization problem. The standard implementation relies on the evolution being adiabatic: keeping the system in the instantaneous ground state with high probability and requiring a time scale inversely related to the minimum energy gap between the instantaneous ground and excited states. However, adiabatic evolution can lead to evolution times that scale exponentially with the system size, even for computationally simple problems. Here, we study whether non-adiabatic evolutions with optimized annealing schedules can bypass this exponential slowdown for one such class of problems called the frustrated ring model. For sufficiently optimized annealing schedules and system sizes of up to 39 qubits, we provide numerical evidence that we can avoid the exponential slowdown. Our work highlights the potential of highly-controllable quantum annealing to circumvent bottlenecks associated with the standard implementation of quantum annealing.

Beyond quantum annealing: optimal control solutions to maxcut problems

“…Regarding future work, we identify two promising avenues for exploration. The first avenue involves applying the techniques discussed to one of the simplest models featuring an exponentially small spectral gap in its spectrum: the frustrated Ising ring model, as introduced in [17] and further explored in [39]. The second direction is to further explore the connection between our digitized solution and the 'shortcut to adiabaticity' mechanism behind a continuous-time approach based on counter-diabatic driving [23].…”

“…In CRAB, the various control functions are expanded in terms of a finite basis set of functions, usually a Fourier basis-but polynomials have also been used [38] -, hence transforming the functional minimization problem into a finite-dimensional optimization. Alternatively, a linear piece-wise decomposition of the schedule between a series of randomly chosen points has been explored [39] to optimize a frustrated Ising ring model [17], which shows an exponentially small gap in the excitation spectrum, thereby posing severe difficulties for QA.…”

Postprocessing Variationally Scheduled Quantum Algorithm for Constrained Combinatorial Optimization Problems

“…It should be noted that previous studies fixed s(0) = 0 and s(T ) = 1, and then used the values of s(t) during quantum simulation as variational parameters [8], [12], [13]. Unlike previous studies, we adopt s 1 and s 2 as variational parameters since the optimal schedule function in the continuous schedule does not always start with s(0) = 0 or end with s(T ) = 1 (see Fig.…”