# Lossy compression of statistical data using quantum annealer

arXiv: https://arxiv.org/abs/2110.02142 · HTML: https://mlsanity.com/paper/2110.02142/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 58 references that are in the map.
- First posted on arXiv 5 Oct 2021.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Lossy Image Compression with Compressive Autoencoders](https://mlsanity.com/paper/1703.00395/) (2017)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [cuSZ: An Efficient GPU-Based Error-Bounded Lossy Compression Framework for Scientific Data](https://mlsanity.com/paper/2007.09625/) (2020)
- [Image classification using quantum inference on the D-Wave 2X](https://mlsanity.com/paper/1905.13215/) (2019)
- [A regression algorithm for accelerated lattice QCD that exploits sparse inference on the D-Wave quantum annealer](https://mlsanity.com/paper/1911.06267/) (2019)
- [Image Compression: Sparse Coding vs. Bottleneck Autoencoders](https://mlsanity.com/paper/1710.09926/) (2017)

## Built on by (most cited first, 4 of 4)

- [Lossy compression of matrices by black-box optimisation of mixed integer nonlinear programming](https://mlsanity.com/paper/2204.10579/) (2022)
- [Prediction and compression of lattice QCD data using machine learning algorithms on quantum annealer](https://mlsanity.com/paper/2112.02120/) (2021)
- [Subsampling Factorization Machine Annealing](https://mlsanity.com/paper/2508.08778/) (2025)
- [Quantum Annealing for Robust Principal Component Analysis](https://mlsanity.com/paper/2501.10431/) (2025)

## Abstract (arXiv)

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.