AUTHOR=Rogers Michael L. , Singleton Robert L. 

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

JOURNAL=Frontiers in Physics

VOLUME=Volume 8 - 2020

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00265

DOI=10.3389/fphy.2020.00265

ISSN=2296-424X

ABSTRACT=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 become very time 
consuming for large matrices, and more efficient computational methods are 
desired. In the twilight of Moore\rq{}s Law, quantum computing is perhaps the 
most direct path out of the darkness. There are two complementary paradigms 
for quantum computing, namely, gated systems and quantum annealers. In this 
paper, we express floating point operations such as division and matrix inversion 
in terms of a {\em 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, but we provide results from the D-Wave quantum
anneler for 2x2 and 3x3 general matrices. Our algorithm 
scales to very large numbers of linear equations. We should also mention that 
our algorithm provides the full solution the the matrix problem, while HHL 
provides only an expectation value.