Impact of memory device precision in analog combinatorial optimization solvers

npj Unconventional Computing, vol. 3

Abstract

Abstract Analog computing methods such as Ising machines may solve challenging optimization problems faster than digital computers, by leveraging energy-minimizing physical dynamics. Problem instances must be mapped to the hardware, including a weight coupling matrix between every spin or neuron in the analog substrate. To represent these weights, some memory technology must be used, such as memristive, magnetic, ferro-electric, or traditional digital memory (e.g., SRAM). We show that precision errors in these couplings can have significant impact on the convergence of solvers, quantifying the impact and illustrating failure mechanisms. We observe that moderate programming errors preserve the global minimum location but can deepen local extrema, slowing down the solver. Under larger errors, severe energy-landscape distortions can occur in which the true ground state becomes unstable and the solver converges to incorrect solutions. Furthermore, different mappings to hardware, such as quadratic versus higher-order representations, can exhibit substantially different precision sensitivity due to the required dynamic range of coupling terms and the introduction of auxiliary variables. Experiments are performed with analog memristive arrays, empirically quantifying the impact of precision on incorrect spin updates. We show increasing problem size sharpens the precision sensitivity, and propose several methods to reduce the impact of such errors.

Authors 6

1. Mohammad Hizzani corresponding Aachen

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Peter Grünberg Institute (PGI-14), Forschungszentrum Jülich GmbH, Jülich, Germany

   RWTH Aachen University, Aachen, Germany

2. Ming-Jay Yang

   Forschungszentrum Jülich

   Affiliation as printed

   Peter Grünberg Institute (PGI-14), Forschungszentrum Jülich GmbH, Jülich, Germany

3. Arne Heittmann

   Forschungszentrum Jülich

   Affiliation as printed

   Peter Grünberg Institute (PGI-14), Forschungszentrum Jülich GmbH, Jülich, Germany

4. George Higgins Hutchinson

   University of California, Santa Barbara

   Affiliation as printed

   Electrical and Computer Engineering, University of California, Santa Barbara, Santa Barbara, CA, USA

5. Dmitri B. Strukov

   University of California, Santa Barbara

   Affiliation as printed

   Electrical and Computer Engineering, University of California, Santa Barbara, Santa Barbara, CA, USA

6. John Paul Strachan corresponding Aachen

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Peter Grünberg Institute (PGI-14), Forschungszentrum Jülich GmbH, Jülich, Germany

   RWTH Aachen University, Aachen, Germany