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Using Spectral Graph Theory to Map Qubits onto Connectivity-limited Devices

Using Spectral Graph Theory to Map Qubits onto Connectivity-limited Devices We propose an efficient heuristic for mapping the logical qubits of quantum algorithms to the physical qubits of connectivity-limited devices, adding a minimal number of connectivity-compliant SWAP gates. In particular, given a quantum circuit, we construct an undirected graph with edge weights a function of the two-qubit gates of the quantum circuit. Taking inspiration from spectral graph drawing, we use an eigenvector of the graph Laplacian to place logical qubits at coordinate locations. These placements are then mapped to physical qubits for a given connectivity. We primarily focus on one-dimensional connectivities and sketch how the general principles of our heuristic can be extended for use in more general connectivities. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Quantum Computing Association for Computing Machinery

Using Spectral Graph Theory to Map Qubits onto Connectivity-limited Devices

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2021 ACM
ISSN
2643-6809
eISSN
2643-6817
DOI
10.1145/3436752
Publisher site
See Article on Publisher Site

Abstract

We propose an efficient heuristic for mapping the logical qubits of quantum algorithms to the physical qubits of connectivity-limited devices, adding a minimal number of connectivity-compliant SWAP gates. In particular, given a quantum circuit, we construct an undirected graph with edge weights a function of the two-qubit gates of the quantum circuit. Taking inspiration from spectral graph drawing, we use an eigenvector of the graph Laplacian to place logical qubits at coordinate locations. These placements are then mapped to physical qubits for a given connectivity. We primarily focus on one-dimensional connectivities and sketch how the general principles of our heuristic can be extended for use in more general connectivities.

Journal

ACM Transactions on Quantum Computing – Association for Computing Machinery

Published: Feb 10, 2021

Keywords: Compilation

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