Experimental Demonstration of a Reconfigurable Coupled Oscillator Platform to Solve the Max-Cut Problem

• Published in: IEEE journal on exploratory solid-state computational devices and circuits Vol. 6; no. 2; pp. 116 - 121
• Main Authors: Bashar, Mohammad Khairul, Mallick, Antik, Truesdell, Daniel S., Calhoun, Benton H., Joshi, Siddharth, Shukla, Nikhil
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01-12-2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Analog; Boolean algebra; Capacitors; Combinatorial analysis; coupled oscillators; Coupling; Graphs; integrated circuit (IC); Integrated circuits; Ising machines; maximum cut (Max-Cut); NP-hard problem; Optimization; Oscillators; Reconfigurable architectures; Reconfiguration; Relaxation oscillators; Room temperature
• ISSN: 2329-9231; 2329-9231
• DOI: 10.1109/JXCDC.2020.3025994

In this work, we experimentally demonstrate an integrated circuit (IC) of 30 relaxation oscillators with reconfigurable capacitive coupling to solve the NP-Hard maximum cut (Max-Cut) problem. We show that under the influence of an external second-harmonic injection signal, the oscillator phases exhibit a bipartition that can be used to calculate a high-quality approximate Max-Cut solution. Leveraging the all-to-all reconfigurable coupling architecture, we experimentally evaluate the computational properties of the oscillators using randomly generated graph instances of varying size and edge density (<inline-formula> <tex-math notation="LaTeX">\eta </tex-math></inline-formula>). Furthermore, comparing the Max-Cut solutions with the optimal values, we show that the oscillators (after simple postprocessing) produce a Max-Cut that is within 99% of the optimal value in 28 of the 36 measured graphs; importantly, the oscillators are particularly effective in dense graphs with the Max-Cut being optimal in seven out of nine measured graphs with <inline-formula> <tex-math notation="LaTeX">\eta =0.8 </tex-math></inline-formula>. Our work marks a step toward creating an efficient, room-temperature-compatible non-Boolean hardware-based solver for hard combinatorial optimization problems.