Floating-Point Calculations on a Quantum Annealer: Division and Matrix Inversion

作     者：Rogers, Michael L. Singleton, Robert L., Jr. 

作者机构：SavantX Santa Fe NM 87501 USA Univ Leeds Sch Math Leeds W Yorkshire England 

出 版 物：《FRONTIERS IN PHYSICS》 (Front. Phys.)

年 卷 期：2020年第8卷

核心收录：

基　　金：ASC Beyond Moore's Law Project at LANL 

主　　题：quantum computing matrix inversion quantum annealing algorithm linear algebra algorithms D-wave 

摘      要：Systems of linear equations are employed almost universally across a wide range of disciplines, from physics and engineering to biology, chemistry, and statistics. Traditional solution methods such as Gaussian elimination are very time consuming for large matrices, and more efficient computational methods are desired. In the twilight of Moore s Law, quantum computing is perhaps the most direct path out of the darkness. There are two complementary paradigms for quantum computing, namely, circuit-based systems and quantum annealers. In this paper, we express floating point operations, such as division and matrix inversion, in terms of a quadratic unconstrained binary optimization (QUBO) problem, a formulation that is ideal for a quantum annealer. We first address floating point division, and then move on to matrix inversion. We provide a general algorithm for any number of dimensions, and, as a proof-of-principle, we demonstrates results from the D-Wave quantum annealer for 2 x 2 and 3 x 3 general matrices. In principle, our algorithm scales to very large numbers of linear equations;however, in practice the number is limited by the connectivity and dynamic range of the machine.