Multistart Methods for Quantum Approximate optimization

Abstract

Hybrid quantum-classical algorithms such as the quantum approximate optimization algorithm (QAOA) are considered one of the most promising approaches for leveraging near-term quantum computers for practical applications. Such algorithms are often implemented in a variational form, combining classical optimization methods with a quantum machine to find parameters to maximize performance. The quality of the QAOA solution depends heavily on quality of the parameters produced by the classical optimizer. Moreover, the presence of multiple local optima in the space of parameters makes it harder for the classical optimizer. In this paper we study the use of a multistart optimization approach within a QAOA framework to improve the performance of quantum machines on important graph clustering problems. We also demonstrate that reusing the optimal parameters from similar problems can improve the performance of classical optimization methods, expanding on similar results for MAXCUT.

Evaluating Quantum Approximate Optimization Algorithm: A Case Study

“…We use derivativefree Bound Optimization BY Quadratic Approximation (BOBYQA) [14] as implemented in the NLopt nonlinearoptimization package [15]. BOBYQA was shown to perform well for QAOA parameter optimization [16] as compared to other off-the-shelf derivative-free optimization methods. We set the tolerances on change in the function value to 10 −3 and on the change in optimization parameters to 10 −2 .…”

Multiblock ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers

“…On the other hand, some encouraging results in terms of performance advantage of QAOA with respect to the classical Goemans-Williamson limit have appeared [60]. In addition, the combination of hyperparametrization and multistart strategies has shown promising results in escaping local optima [61]. These considerations, together with the fact that QAOA is not efficiently simulatable by classical computers, make QAOA an appealing algorithm to explore on noisy quantum machines.…”

Quantum Algorithms for Mixed Binary Optimization Applied to Transaction Settlement

“…The energy landscapes of the QAOA and the VQE are typically non-convex and contain many local minima. Current research has focused on strategies such as reinforcement learning [25] and multi-start methods [26] to navigate this landscape. The quality of the VQE and QAOA solutions increases with the depth of the quantum algorithm [23] which can lead to deep quantum circuits which exhaust the coherence time of noisy quantum hardware.…”