  We present a new lossy compression algorithm for statistical floating-point
data through a representation learning with binary variables. The algorithm
finds a set of basis vectors and their binary coefficients that precisely
reconstruct the original data. The optimization for the basis vectors is
performed classically, while binary coefficients are retrieved through both
simulated and quantum annealing for comparison. A bias correction procedure is
also presented to estimate and eliminate the error and bias introduced from the
inexact reconstruction of the lossy compression for statistical data analyses.
The compression algorithm is demonstrated on two different datasets of lattice
quantum chromodynamics simulations. The results obtained using simulated
annealing show 3.5 times better compression performance than the algorithms
based on a neural-network autoencoder and principal component analysis.
Calculations using quantum annealing also show promising results, but
performance is limited by the integrated control error of the quantum
processing unit, which yields large uncertainties in the biases and coupling
parameters. Hardware comparison is further studied between the previous
generation D-Wave 2000Q and the current D-Wave Advantage system. Our study
shows that the Advantage system is more likely to obtain low-energy solutions
for the problems than the 2000Q.
