Abstract
Networks of coupled parametric resonators (parametrons) hold promise for parallel computing architectures. En route to realizing complex networks, we report an experimental and theoretical analysis of two coupled parametrons. In contrast to previous studies, we explore the case of strong bilinear coupling between the parametrons, as well as the role of detuning. We show that the system can still operate as an Ising machine in this regime, even though careful calibration is necessary to ensure that the correct solution space is available. Apart from the formation of split normal modes, new states of mixed symmetry are generated. Furthermore, we predict that systems with $N>2$ parametrons will undergo multiple phase transitions before arriving at a regime that can be equivalent to the Ising problem.
Highlights
Driven nonlinear systems were first considered as logic elements at the dawn of the digital era [1–3]
Experimental setup: We built a setup of capacitively coupled parametrons using electrical lumped-element resonators, see Fig. 2(a)
Using Kirchhoff’s laws, our electrical circuits are described by coupled equations of motion [15], xi + ωi2[1 − λ cos (2ωdt )]xi + αixi3 + γixi − Ji jx j = 0
Summary
Driven nonlinear systems were first considered as logic elements at the dawn of the digital era [1–3]. Under the influence of a parametric drive and the node coupling, the entire system evolves towards a stable “optimal” configuration, i.e., a particular oscillation mode involving all resonators The proposals rely on the notion of (quantum) adiabatic state evolution, which implies that the damping rate γ is the smallest energy scale in the system; in particular, this requires that the coupling dominates over the dissipation This condition, which is commonly referred to as “strong coupling,” ensures that the exchange of energy (and information) between individual resonators is faster than the loss-induced decoherence of the network. For N > 2 parametrons, the normal-mode perspective allows us to predict a surprising problem, arising in all instances of Ising machines: the number of available network solutions does not scale with 2N close to threshold. We discuss this “state space” problem along with a potential explanation to reconcile our findings with the operational functionality of an Ising machine
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