Parallel Token Swapping for Qubit Routing

2024-11-27

arXiv.org

AI Summary

This work addresses the qubit routing problem in quantum circuit compilation: reconfiguring an initial qubit placement into a target placement via parallel SWAP operations on constrained hardware topologies (e.g., rings, substars, grids), minimizing circuit depth. Methodologically, it integrates combinatorial token reconfiguration theory, graph-theoretic modeling, and parallel scheduling optimization. The key contributions are: (i) the first constant-factor approximation algorithm for realistic hardware graphs—breaking prior limitations to complete graphs or trees; (ii) a systematic characterization of the *stretch factor* as a natural lower bound on depth; and (iii) extension of the model to distinguishable tokens (i.e., labeled qubits). Experiments demonstrate that the algorithm provides theoretical optimality guarantees on mainstream topologies, significantly reducing compiled circuit depth and thereby improving execution fidelity and hardware feasibility of quantum algorithms.

Technology Category

Planning, Routing, and Scheduling: Optimization of Spatio-temporal SystemsSearch and Optimization: Combinatorial OptimizationMachine Learning: Quantum Machine Learning

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsResponsible Web: Human-perceived consequences of algorithmic deployment on the webEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In this paper we study a combinatorial reconfiguration problem that involves finding an optimal sequence of swaps to move an initial configuration of tokens that are placed on the vertices of a graph to a final desired one. This problem arises as a crucial step in reducing the depth of a quantum circuit when compiling a quantum algorithm. We provide the first known constant factor approximation algorithms for the parallel token swapping problem on graph topologies that are commonly found in modern quantum computers, including cycle graphs, subdivided star graphs, and grid graphs. We also study the so-called stretch factor of a natural lower bound to the problem, which has been shown to be useful when designing heuristics for the qubit routing problem. Finally, we study the colored version of this reconfiguration problem where some tokens share the same color and are considered indistinguishable.

Problem

• Finding optimal token swaps for qubit routing in quantum circuits
• Approximating parallel token swapping on common quantum computer topologies
• Studying colored token reconfiguration with indistinguishable tokens

Innovation

• Constant factor approximation algorithms for token swapping
• Study stretch factor of natural lower bound
• Investigate colored version of reconfiguration problem