A regression algorithm for accelerated lattice QCD that exploits sparse inference on the D-Wave quantum annealer

We propose a regression algorithm that utilizes a learned dictionary optimized for sparse inference on D-Wave quantum annealer. In this regression algorithm, we concatenate the independent and dependent variables as an combined vector, and encode the high-order correlations between them into a dictionary optimized for sparse reconstruction. On a test dataset, the dependent variable is initialized to its average value and then a sparse reconstruction of the combined vector is obtained in which the dependent variable is typically shifted closer to its true value, as in a standard inpainting or denoising task. Here, a quantum annealer, which can presumably exploit a fully entangled initial state to better explore the complex energy landscape, is used to solve the highly non-convex sparse coding optimization problem. The regression algorithm is demonstrated for a lattice quantum chromodynamics simulation data using a D-Wave 2000Q quantum annealer and good prediction performance is achieved. The regression test is performed using six different values for the number of fully connected logical qubits, between 20 and 64, the latter being the maximum that can be embedded on the D-Wave 2000Q. The scaling results indicate that a larger number of qubits gives better prediction accuracy, the best performance being comparable to the best classical regression algorithms reported so far.