Improving Quantum Computation by Optimized Qubit Routing

TL;DR

This paper introduces a novel decomposition approach for qubit routing in quantum computing, improving solution quality and reducing circuit depth and gates, thereby enhancing performance on real hardware.

Contribution

It presents a new decomposition method combining allocation and token swapping, with exact algorithms and bounds, leading to faster, near-optimal routing solutions that outperform existing heuristics.

Findings

Solutions are fast and close to optimal.

Significant reduction in gates and circuit depth.

Improved solution quality on real hardware.

Abstract

In this work we propose a high-quality decomposition approach for qubit routing by swap insertion. This optimization problem arises in the context of compiling quantum algorithms onto specific quantum hardware. Our approach decomposes the routing problem into an allocation subproblem and a set of token swapping problems. This allows us to tackle the allocation part and the token swapping part separately. Extracting the allocation part from the qubit routing model of Nannicini et al. (arXiv:2106.06446), we formulate the allocation subproblem as a binary program. Herein, we employ a cost function that is a lower bound on the overall routing problem objective. We strengthen the linear relaxation by novel valid inequalities. For the token swapping part we develop an exact branch-and-bound algorithm. In this context, we improve upon known lower bounds on the token swapping problem. Furthermore, we enhance an existing approximation algorithm. We present numerical results for the integrated allocation and token swapping problem. Obtained solutions may not be globally optimal due to the decomposition and the usage of an approximation algorithm. However, the solutions are obtained fast and are typically close to optimal. In addition, there is a significant reduction in the number of gates and output circuit depth when compared to state-of-the-art heuristics. Reducing these figures is crucial for minimizing noise when running quantum algorithms on near-term hardware. As a consequence, using the novel decomposition approach leads to compiled algorithms with improved quality. Indeed, when compiled with the novel routing procedure and executed on real hardware, our experimental results for quantum approximate optimization algorithms show an significant increase in solution quality in comparison to standard routing methods.