New approach brings scientists one step closer to practical quantum computing
Quantum computers have arisen as a possible solution for highly complex mathematical problems, offering “quantum advantage” over classical computers in certain cases. The Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate for realizing this advantage, and some success has been achieved for small problems. But demonstrations on large problems have remained too computationally costly to run on classical computers and current quantum hardware.
Researchers from JPMorganChase and the U.S. Department of Energy’s (DOE) Argonne National Laboratory have now found a way to make such calculations possible. Their results were published in Physical Review Letters.
Overcoming the computational barrier
The team focused on the Sherrington–Kirkpatrick (SK) model, a disordered system with random interactions between every pair of variables.
“As problem size grows, the SK model’s optimal value is known in the large-system limit. This value provides a baseline to measure how well QAOA is performing,” said Jeffrey Larson, a computational mathematician in Argonne’s Mathematics and Computer Science division and a coauthor of the paper.
The researchers discovered that in the infinite-size limit, a high-depth QAOA state for the SK model converges mathematically to a single quantum spin coupled to bosonic modes. By translating the problem into this “spin-boson” system, the team replaced the costly calculations with much simpler simulations using matrix product state simulations.
For this problem setting, Larson developed a novel optimization method for identifying high-quality QAOA parameters. The simulations and parameter optimization were performed on the supercomputers at the Argonne Leadership Computing Facility (ALCF) and DOE’s National Energy Research Scientific Computing Center. The researchers were able to use these facilities through a grant from the DOE’s Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program. The ALCF is a DOE Office of Science user facility.
“This multi-institutional collaboration is a great way to work because the questions are both practical and fundamental,” Larson said. “We are asking how far quantum optimization algorithms can go, and we need advanced classical simulation, strong optimization tools and high-performance computing to understand what is really possible.”
A new pathway for quantum computing studies
The new technique lets researchers evaluate the expected solution quality of QAOA without running it end to end.
“Progress in quantum computing is not just about building larger devices,” Larson said. “It also depends on better algorithms, better optimization methods and better classical tools for testing and understanding those algorithms.”
The researchers believe their results lay a foundation for understanding the potential and limitations of quantum optimization algorithms as quantum hardware matures.
For more details, see the full paper by Sami Boulebnane, Abid Khan, Minzhao Liu, Jeffrey Larson, Dylan Herman, Ruslan Shaydulin, and Marco Pistoia, “Spin-Boson Mapping of the Quantum Approximate Optimization Algorithm,” Physical Review Letters 136, 240601 https://doi.org/10.1103/2w94-rymn. A preprint is available at https://arxiv.org/abs/2505.07929.
Argonne National Laboratory seeks solutions to pressing national problems in science and technology by conducting leading-edge basic and applied research in virtually every scientific discipline. Argonne is managed by UChicago Argonne, LLC for the U.S. Department of Energy’s Office of Science.
The U.S. Department of Energy’s Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit https://energy.gov/science.