The Quantum Artificial Intelligence Lab (QuAIL) team has successfully trained a quantum computer to generate (low-resolution) handwritten digits. The QuAIL team trained the D-Wave 2X quantum computer hosted at NASA Ames Research Center to achieve this task and is the first team in the world to successfully do so.

An image can be represented in a computer as an array of pixels; the color of each pixel can be encoded in a number. A black and white picture, for instance, can be represented as an array of binary variables. Computer generation of a set of digit images resembling handwritten digits can be thought of as generating a sample array of variables from a complex, high-dimensional probability distribution; but which distribution? There are machine-learning algorithms that allow a computer to "learn" the right probability distribution from a set of sample images. Such algorithms rely heavily on sampling from the model probability distribution. There is increasing interest in the potential advantages of using quantum computing technologies as sampling engines to speedup these tasks. However, several limitations have previously barred these state-of-the-art technologies from being used effectively. The QuAIL team has managed to surpass these bottlenecks. The work has been summarized in a paper that can be found at the preprint server ArXiv.org: Quantum-Assisted Learning of Graphical Models With Arbitrary Pairwise Connectivity

**BACKGROUND**: NASA’s QuAIL team aims to demonstrate that quantum computing and quantum algorithms may someday dramatically improve the Agency’s ability to solve difficult optimization problems for missions in aeronautics, Earth and space sciences, and space exploration. One of the central open questions in the field of quantum computing is the existence of efficient quantum heuristic algorithms for solving classically intractable instances of combinatorial optimization problems that are found at the core of many of NASA’s missions. Classical heuristic algorithms have been developed over the years to solve or approximate solutions to practical instances of hard problems, and the search for improved heuristics remains an active research area. The efficacy of these approaches is generally determined by running them on benchmark sets of problem instances. Such empirical testing for quantum algorithms requires the availability of quantum hardware. NASA’s QuAIL team uses the D-Wave Vesuvius processor, which is cooled to 20 millikelvin (near absolute zero) to design and evaluate quantum approaches to challenging combinatorial optimization problems. The hope is that quantum computing will vastly improve a wide range of tasks that can lead to new discoveries and technologies, some of which may significantly change the way we solve real-world problems.

**NASA PROGRAM FUNDING**: This work was supported in part by NASA Ames Research Center under Contract Numbers NNA14AA60C and NAS2-03144, an Air Force Research Lab (AFRL) Information Directorate under grant number F4HBKC4162G001, the Office of the Director of National Intelligence (ODNI), and the Intelligence Advanced Research Projects Activity (IARPA), via IAA number 145483.

**TEAM**: Marcello Benedetti, Rupak Biswas, Alejandro Perdomo-Ortiz, and John Realpe-Gomez

**POINT OF CONTACT**: John Realpe-Gomez, john.e.realpegomez@nasa.gov