Quantum annealing for systems of polynomial equations

Journal Article · 16 July 2019 · Scientific Reports

DOI: https://doi.org/10.1038/s41598-019-46729-0 · OSTI ID:1619570

Chang, Chia Cheng ; Gambhir, Arjun; Humble, Travis S.; Sota, Shigetoshi

Abstract Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct matrix inversion or iteratively with judicious preconditioning. However, the convergence of iterative algorithms is highly variable and depends, in part, on the condition number. We present a direct method for solving general systems of polynomial equations based on quantum annealing, and we validate this method using a system of second-order polynomial equations solved on a commercially available quantum annealer. We then demonstrate applications for linear regression, and discuss in more detail the scaling behavior for general systems of linear equations with respect to problem size, condition number, and search precision. Finally, we define an iterative annealing process and demonstrate its efficacy in solving a linear system to a tolerance of 10 ⁻⁸ .

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE; USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC)
• Grant/Contract Number: AC02-05CH11231; AC05-00OR22725; AC52-07NA27344
• OSTI ID: 1619570
• Report Number(s): LLNL-JRNL--761230; 10258; PII: 46729
• Journal Information: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 9; ISSN 2045-2322
• Publisher: Nature Publishing GroupCopyright Statement
• Country of Publication: United Kingdom
• Language: English