Quantum optimization algorithm for solving elliptic boundary value problems on D-Wave quantum annealing device

Rebecca Conley; Deokkyu Choi; Gregory Medwig; Eric Mroczko; David Wan; Paulo Castillo; Kwangmin Yu

doi:10.1117/12.2649076

8 March 2023 Quantum optimization algorithm for solving elliptic boundary value problems on D-Wave quantum annealing device

Rebecca Conley, Deokkyu Choi, Gregory Medwig, Eric Mroczko, David Wan, Paulo Castillo, Kwangmin Yu

Author Affiliations +

Proceedings Volume 12446, Quantum Computing, Communication, and Simulation III; 124460A (2023) https://doi.org/10.1117/12.2649076
Event: SPIE Quantum West, 2023, San Francisco, California, United States

Abstract

The quantum annealing devices, which encode the solution to a computational problem in the ground state of a quantum Hamiltonian, are implemented in D-Wave systems with more than 2,000 qubits. However, quantum annealing can solve only a classical combinatorial optimization problem such as an Ising model, or equivalently, a quadratic unconstrained binary optimization (QUBO) problem. In this paper, we formulate the QUBO model to solve elliptic problems with Dirichlet and Neumann boundary conditions using the finite element method. In this formulation, we develop the objective function of quadratic binary variables represented by qubits and the system finds the binary string combination minimizing the objective function globally. Based on the QUBO formulation, we introduce an iterative algorithm to solve the elliptic problems. We discuss the validation of the modeling on the D-Wave quantum annealing system.

Conference Presentation

Citation Download Citation

Rebecca Conley, Deokkyu Choi, Gregory Medwig, Eric Mroczko, David Wan, Paulo Castillo, and Kwangmin Yu "Quantum optimization algorithm for solving elliptic boundary value problems on D-Wave quantum annealing device", Proc. SPIE 12446, Quantum Computing, Communication, and Simulation III, 124460A (8 March 2023); https://doi.org/10.1117/12.2649076

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available