Affiliation:
1. IonQ, Inc., College Park, MD 20740, USA
Abstract
This paper presents a system for solving binary-valued linear equations using quantum computers. The system is called Mod2VQLS, which stands for Modulo 2 Variational Quantum Linear Solver. As far as we know, this is the first such proposal. The design is a classical–quantum hybrid. The quantum components are a new circuit design for implementing matrix multiplication modulo 2, and a variational circuit to be optimized. The classical components are the optimizer, which measures the cost function and updates the quantum parameters for each iteration, and the controller that runs the quantum job and classical optimizer iterations. We propose two alternative ansatze or templates for the variational circuit and present results showing that the rotation ansatz designed specifically for this problem provides the most direct path to a valid solution. Numerical experiments in low dimensions indicate that Mod2VQLS, using the custom rotations ansatz, is on par with the block Wiedemann algorithm, which is the best-known to date solution for this problem.
Subject
Fluid Flow and Transfer Processes,Computer Science Applications,Process Chemistry and Technology,General Engineering,Instrumentation,General Materials Science
Reference42 articles.
1. A tale of two sieves;Pomerance;Not. Am. Math. Soc.,1996
2. Aboumrad, W., Widdows, D., and Kaushik, A. (2023). Quantum and Classical Combinatorial Optimizations Applied to Lattice-Based Factorization. arXiv.
3. Schuld, M., and Petruccione, F. (2021). Machine Learning with Quantum Computers, Springer.
4. Trefethen, L.N., and Bau, D. (1997). Numerical Linear Algebra, S.I.A.M.
5. Boudot, F., Gaudry, P., Guillevic, A., Heninger, N., Thome, E., and Zimmermann, P. (2020, January 17–21). Comparing the difficulty of factorization and discrete logarithm: A 240-digit experiment. Proceedings of the Advances in Cryptology–CRYPTO 2020: 40th Annual International Cryptology Conference, CRYPTO 2020, Santa Barbara, CA, USA.