Divide and Conquer for Combinatorial Optimization and Distributed Quantum Computation

Scaling the size of monolithic quantum computer systems is a difficult task. As the number of qubits within a device increases, a number of factors contribute to decreases in yield and performance. To meet this challenge, distributed architectures composed of many networked quantum computers have been proposed as a viable path to scalability. Such systems will need algorithms and compilers that are tailored to their distributed architectures. In this work we introduce the Quantum Divide and Conquer Algorithm (QDCA), a hybrid variational approach to mapping large combinatorial optimization problems onto distributed quantum architectures. This is achieved through the combined use of graph partitioning and quantum circuit cutting. The QDCA, an example of application-compiler co-design, alters the structure of the variational ansatz to tame the exponential compilation overhead incurred by quantum circuit cutting. The result of this cross-layer co-design is a highly flexible algorithm which can be tuned to the amount of classical or quantum computational resources that are available, and can be applied to both near- and long-term distributed quantum architectures. We simulate the QDCA on instances of the Maximum Independent Set problem and find that it is able to outperform similar classical algorithms. We also evaluate an 8-qubit QDCA ansatz on a superconducting quantum computer and show that circuit cutting can help to mitigate the effects of noise. Our work demonstrates how many small-scale quantum computers can work together to solve problems $85\%$ larger than their own qubit count, motivating the development and potential of large-scale distributed quantum computing.