From Exponential to Quadratic: Optimal Control for a Frustrated Ising Ring Model

TL;DR

This paper demonstrates that a frustrated Ising ring model can be optimally solved using digital quantum algorithms with quadratic resource scaling, improving solution accuracy over traditional methods.

Contribution

It introduces a digital control approach for the frustrated Ising ring, achieving exact solutions with quadratic resource scaling using QAOA and CRAB techniques.

Findings

Quadratic scaling of resources for exact solutions.

High-accuracy solutions with combined CRAB and digitized annealing.

Digital control makes the model efficiently solvable with quantum algorithms.

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 showing exponentially small spectral gaps was introduced by Roberts et al., PRA 101, 042317 (2020): a ferromagnetic Ising ring with a single frustrating antiferromagnetic bond. A previous study of this model (C\^ot\'e et al., QST 8, 045033 (2023)) proposed a 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 (QAOA); 2) We combine a technique of quantum control -- the Chopped RAndom Basis (CRAB) method -- and digitized quantum annealing (dQA) to construct smooth digital schedules yielding optimal solutions with very high accuracy.