Multidimensional hyperspin machine

Abstract

From condensed matter to quantum chromodynamics, multidimensional spins are a fundamental paradigm, with a pivotal role in combinatorial optimization and machine learning. Machines formed by coupled parametric oscillators can simulate spin models, but only for Ising or low-dimensional spins. Currently, machines implementing arbitrary dimensions remain a challenge. Here, we introduce and validate a hyperspin machine to simulate multidimensional continuous spin models. We realize high-dimensional spins by pumping groups of parametric oscillators, and show that the hyperspin machine finds to a very good approximation the ground state of complex graphs. The hyperspin machine can interpolate between different dimensions by tuning the coupling topology, a strategy that we call “dimensional annealing”. When interpolating between the XY and the Ising model, the dimensional annealing substantially increases the success probability compared to conventional Ising simulators. Hyperspin machines are a new computational model for combinatorial optimization. They can be realized by off-the-shelf hardware for ultrafast, large-scale applications in classical and quantum computing, condensed-matter physics, and fundamental studies.

Ising Dynamics for Programmable Threshold Sensing in Wireless Devices

“…As a result, they express two possible solutions for input power levels higher than 𝑃 𝑡ℎ : one stable and one unstable. These solutions are phase-shifted by 𝜋 with respect to each other and, in the absence of noise, can be reached equiprobably 32 (see Supplementary Section II). When two POs are coupled by an impedance 𝑍 𝐶 in Fig.…”

“…In the realm of optimization, the Ising model has been employed to describe the collective behavior of dissipatively coupled parametric oscillators (POs) [27][28][29][30][31] . Within this framework, studies have revealed that a network of resistively coupled electrical POs naturally converges towards a collective oscillation state that minimizes a Lyapunov function 32,33 . This allows the network to evolve towards the ground state configuration of its Hamiltonian, enabling the use of networks of POs to solve combinatorial optimization problems 27,29,[32][33][34] .…”

“…Within this framework, studies have revealed that a network of resistively coupled electrical POs naturally converges towards a collective oscillation state that minimizes a Lyapunov function 32,33 . This allows the network to evolve towards the ground state configuration of its Hamiltonian, enabling the use of networks of POs to solve combinatorial optimization problems 27,29,[32][33][34] . While Ising systems formed by dissipatively coupled POs have been previously studied, only a few studies 28,33 have looked at the exploitation of the same dynamics exploited by these Ising systems in networks of POs coupled by dispersive frequency-dependent components, and these prior works are predominantly theoretical only.…”

“…In this state, they generate equal-magnitude subharmonic signals with frequency 𝑓 𝑝 /2 and phase-difference (∆𝜙) equal to 0 or 𝜋 depending on the value of the sensed PoI [see Fig. 1(e)] 31,32 .…”

Feedback and constraints in physical optimizers

“…It is interesting to note that these algorithms thus seem to keep a set of optimization parameters (the 𝐽𝐽 𝑖𝑖𝑖𝑖 matrix) fixed while interpolating between two distinct domains for the optimization variables -starting with real values allowed but ending with a restriction to binary values. Recently, more general domain interpolations 7,8 have been investigated for CIM variants.…”