From exponential to quadratic: optimal control for a frustrated Ising ring model

Abstract

Exponentially small spectral gaps are known to be the crucial bottleneck for traditional Quantum Annealing (QA) based on interpolating between two Hamiltonians, a simple driving term and the complex problem to be solved, with a linear schedule in time. One of the simplest models exhibiting exponentially small spectral gaps is a ferromagnetic Ising ring with a single antiferromagnetic bond introducing frustration. Previous studies of this model have explored continuous-time diabatic QA, where optimized non-adiabatic annealing schedules provided good solutions, avoiding exponentially large annealing times. In our work, we move to a digital framework of Variational Quantum Algorithms, and present two main results: (1) we show that the model is digitally controllable with a scaling of resources that grows quadratically with the system size, achieving the exact solution using the Quantum Approximate Optimization Algorithm; (2) We combine a technique of quantum control—the Chopped RAndom Basis method—and digitized quantum annealing to construct smooth digital schedules yielding optimal solutions with very high accuracy.