  We propose a regression algorithm that utilizes a learned dictionary
optimized for sparse inference on a D-Wave quantum annealer. In this regression
algorithm, we concatenate the independent and dependent variables as a 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 scaling
results indicate that a larger number of qubits gives better prediction
accuracy.
