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.
Hyperspin 2.0
The critical ups and downs are not disorganized, there are symmetries and gauge invariance. They govern the fluctuation process and determine the rule of the structure adjustment. What forms will the critical fluctuation be? What symmetries will follow? In this paper we will investigate the two questions. In Section 2, we put forward three theorems on the critical fluctuations, then two new concepts, isomorph spin and hyperspin, are proposed. In Section 3, we discuss SU(3) symmetries including octet and decuplet states, introduce quablocks and pioblocks, find out abnormal symmetries and three transition temperatures by analysis on symmetries. We predict the influence of these transition temperatures on the quantum field theory. Section 4 is conclusion remark. 2ff7e9595c
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