Scaling Up the Quantum Divide and Conquer Algorithm for Combinatorial Optimization

TL;DR

This paper introduces DC-QDCA, a quantum algorithm that reduces inter-device communication for large graph optimization problems, enabling larger problem sizes with maintained solution quality on quantum simulators.

Contribution

The paper presents a novel Deferred Constraint Quantum Divide and Conquer Algorithm that simplifies quantum circuit topology, allowing scalable quantum optimization for larger problem instances.

Findings

Constructed circuits nearly three times larger than previous methods.

Retained similar or better solution quality with larger problem sizes.

Demonstrated effectiveness on quantum simulators.

Abstract

Quantum optimization as a field has largely been restricted by the constraints of current quantum computing hardware, as limitations on size, performance, and fidelity mean most non-trivial problem instances won't fit on quantum devices. Even proposed solutions such as distributed quantum computing systems may struggle to achieve scale due to the high cost of inter-device communication. To address these concerns, we propose Deferred Constraint Quantum Divide and Conquer Algorithm (DC-QDCA), a method for constructing quantum circuits which greatly reduces inter-device communication costs for some quantum graph optimization algorithms. This is achieved by identifying a set of vertices whose removal partitions the input graph, known as a separator; by manipulating the placement of constraints associated with the vertices in the separator, we can greatly simplify the topology of the optimization circuit, reducing the number of required inter-device operations. Furthermore, we introduce an iterative algorithm which builds on these techniques to find solutions for problems with potentially thousands of variables. Our experimental results using quantum simulators have shown that we can construct tractable circuits nearly three times the size of previous QDCA methods while retaining a similar or greater level of quality.