Creating electronic oscillator-based Ising machines without external injection locking

Abstract

Coupled electronic oscillators have recently been explored as a compact, integrated circuit- and room temperature operation-compatible hardware platform to design Ising machines. However, such implementations presently require the injection of an externally generated second-harmonic signal to impose the phase bipartition among the oscillators. In this work, we experimentally demonstrate a new electronic autaptic oscillator (EAO) that uses engineered feedback to eliminate the need for the generation and injection of the external second harmonic signal to minimize the Ising Hamiltonian. Unlike conventional relaxation oscillators that typically decay with a single time constant, the feedback in the EAO is engineered to generate two decay time constants which effectively helps generate the second harmonic signal internally. Using this oscillator design, we show experimentally, that a system of capacitively coupled EAOs exhibits the desired bipartition in the oscillator phases without the need for any external second harmonic injection, and subsequently, demonstrate its application in solving the computationally hard Maximum Cut (MaxCut) problem. Our work not only establishes a new oscillator design aligned to the needs of the oscillator Ising machine but also advances the efforts to creating application specific analog computing platforms.

Simulated bifurcation assisted by thermal fluctuation

“…x i (t k+1 ) = g(x i ) , (18) ỹi = h(x i , ỹi ) , (19) where the functions g(x) and h(x, y) are given by…”

“…Special-purpose hardware devices for the Ising problem are called Ising machines. Ising machines utilizing natural phenomena have been developed, such as quantum annealers [3][4][5][6][7][8] with superconducting circuits [9], coherent Ising machines with pulse lasers [10][11][12][13][14], oscillator-based Ising machines [15][16][17][18][19], and other Ising machines with various systems, such as stochastic nanomagnets [20], gain-dissipative systems [21], spatial light modulators [22], memristor Hopfield neural networks [23], and spin torque nano-oscillators [24,25].…”

A network‐theoretical perspective on oscillator‐based Ising machines

“…3 Their hardware implementation is commonly based on a network of diffusively coupled (nonlinear) oscillators. [4][5][6][7][8] Although in recent years, we have also seen a number of optical implementations, so-called coherent Ising machines. [9][10][11][12] In principle, all Ising machines are built, such that they have the natural tendency to minimize a scalar function, the so-called Ising Hamiltonian, which relates to the Ising model 13 and describes the energy of a lattice consisting of magnetically coupled spins,…”

“…In this context, oscillator‐based Ising machines are a promising approach for solving combinatorial optimization problems with a large solution space 3 . Their hardware implementation is commonly based on a network of diffusively coupled (nonlinear) oscillators 4–8 . Although in recent years, we have also seen a number of optical implementations, so‐called coherent Ising machines 9–12 …”

A Network-Theoretical Perspective on Oscillator-Based Ising Machines

“…In this context, oscillator-based Ising machines are a promising approach for solving combinatorial optimization problems with a large solution space 3 . Their hardware implementation is commonly based on a network of diffusively coupled (nonlinear) oscillators 4,5,6,7,8 . Although in recent years, we have also seen a number of optical implementations, so-called coherent Ising machines 9,10,11,12 .…”