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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.
Highlights
The Ising model, originally developed for spin glass s ystems[1], has recently experienced renewed attention owing to its application in accelerating computationally hard problems which are still considered intractable to solve using conventional digital computers
Consider the combinatorial optimization-based Maximum Cut (MaxCut) problem—the benchmark problem considered in this work—which entails computing a cut that divides the nodes of the graph in two sets (S1, S2) such that the number of common edges among the two sets is as large as possible
We propose a novel electronic autaptic oscillator (EAO) design that eliminates the need for second harmonic injection; the prefix ‘autaptic’ is inspired from the autapse structures found in biological spiking neurons which are synapses from the excitatory neuron onto itself and provide feedback to regulate the neuron’s spiking activity[36,37,38,39]
Summary
The Ising model, originally developed for spin glass s ystems[1], has recently experienced renewed attention owing to its application in accelerating computationally hard problems which are still considered intractable to solve using conventional digital computers This is motivated by the fact that a large number of such p roblems[2,3,4,5,6] can be directly mapped to the Ising Hamiltonian: H = −. Consider the combinatorial optimization-based Maximum Cut (MaxCut) problem—the benchmark problem considered in this work—which entails computing a cut that divides the nodes of the graph in two sets (S1, S2) such that the number of common edges among the two sets is as large as possible.
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