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

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'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.