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

• Main Authors: Rogers, Michael L, SingletonJr, Robert L
• Format: Journal Article
• Language: English
• Published: 19-01-2019
• Subjects: Physics - Quantum Physics
• DOI: 10.48550/arxiv.1901.06526

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'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 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 $2\times 2$ and $3 \times 3$ 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.