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Proceedings Paper

Approximate graph spectral decomposition with the Variational Quantum Eigensolver
Author(s): Josh Payne; Mario Srouji
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Paper Abstract

Spectral graph theory is a branch of mathematics that studies the relationships between the eigenvectors and eigenvalues of Laplacian and adjacency matrices and their associated graphs. The Variational Quantum Eigen- solver (VQE) algorithm was proposed as a hybrid quantum/classical algorithm that is used to quickly determine the ground state of a Hamiltonian, and more generally, the lowest eigenvalue of a matrix M ∈ Rnxn. There are many interesting problems associated with the spectral decompositions of associated matrices, such as partitioning, embedding, and the determination of other properties. In this paper, we will expand upon the VQE algorithm to analyze the spectra of directed and undirected graphs. We evaluate runtime and accuracy comparisons (empirically and theoretically) between different choices of ansatz parameters, graph sizes, graph densities, and matrix types, and demonstrate the effectiveness of our approach on Rigetti's QCS platform on graphs of up to 64 vertices, finding eigenvalues of adjacency and Laplacian matrices. We finally make direct comparisons to classical performance with the Quantum Virtual Machine (QVM) in the appendix, observing a superpolynomial runtime improvement of our algorithm when run using a quantum computer.*

Paper Details

Date Published: 5 June 2020
PDF: 15 pages
Proc. SPIE 11391, Quantum Information Science, Sensing, and Computation XII, 113910I (5 June 2020); doi: 10.1117/12.2542854
Show Author Affiliations
Josh Payne, Stanford Univ. (United States)
Mario Srouji, Stanford Univ. (United States)


Published in SPIE Proceedings Vol. 11391:
Quantum Information Science, Sensing, and Computation XII
Eric Donkor; Michael Hayduk, Editor(s)

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