Large-scale Quantum Approximate Optimization via Divide-and-Conquer

Abstract

Quantum Approximate Optimization Algorithm (QAOA) is a promising hybrid quantum-classical algorithm for solving combinatorial optimization problems. However, it cannot overcome qubit limitation for large-scale problems. Furthermore, the execution time of QAOA scales exponentially with the problem size. We propose a Divide-and-Conquer QAOA (DC-QAOA) to address the above challenges for graph maximum cut (Max-Cut) problem. The algorithm works by recursively partitioning a larger graph into smaller ones whose MaxCut solutions are obtained with small-size NISQ computers. The overall solution is retrieved from the sub-solutions by applying the combination policy of quantum state reconstruction. Multiple partitioning and reconstruction methods are proposed/ compared. DC-QAOA achieves 97.14% approximation ratio (20.32% higher than classical counterpart), and 94.79% expectation value (15.80% higher than quantum annealing). DC-QAOA also reduces the time complexity of conventional QAOA from exponential to quadratic.

Unsupervised strategies for identifying optimal parameters in Quantum Approximate Optimization Algorithm

“…From an application perspective, we envision these techniques to be employed in algorithms were QAOA is run on a small part of the problem to solve such as divide-and-conquer [9,10] and iterative algorithms [11,12,13]. Restricting to a few number of circuit calls will help decrease the runtime of quantum-featured or quantum-enhanced algorithms, making them closer to compete with classical heuristics.…”

“…Hence, our approaches allow balancing between circuit calls of small quantum computers and performances. Such settings for instance naturally occur in divide-and-conquer-type schemes to enable smaller quantum computers to improve optimization [9,10,11,12], or in Recursive-QAOA [13] as we demonstrate later.…”

“…It exhibits a few properties that makes it interesting for combinatorial optimization [5,6,7,8]. These can be useful when using it as a subroutine [9,10,11,12,13], especially the concentration of parameters [6]. This concentration property suggests that optimal parameters found for one instance can be reused on another.…”

“…On the one hand, the «reasonable» aspect may not be straightforward to characterize [18]. On the other hand, in many QAOAfeatured algorithms [9,10,11,12,13], many instances are generated and could give rise to many distributions. Finally, within a distribution, several areas of concentration may rise.…”

Hybrid Quantum-Classical Algorithms for Loan Collection Optimization with Loan Loss Provisions

“…( 3). The idea is to use a classical divide-andconquer algorithm [22] to arrange the loanees into small groups based on the association matrix. Loanees from the same group will have a higher association compared to those outside the group.…”