Complex Hyperspin Machine and Symmetry Quenching: Benchmark and scaling up to millions of degrees of freedom
Abstract
Driven-dissipative oscillator networks have been proposed to simulate spin models on physical hardware, mostly focusing on systems of binary (Ising) spins, or systems of spin vectors in low dimensions. The equalized hyperspin machine was recently introduced to provide a single platform to simulate general models of N coupled spin vectors with tunable dimension D, realizing dynamical annealing protocols to vary the spin dimensionality in time. These schemes are limited to real spins coupled via real coupling matrices. We propose a generalization of the hyperspin machine that works with complex fields and deals with complex Hermitian coupling matrices, implementing an amplitude equalization scheme. This system, which we name complex hyperspin machine, can work on optimization problems with complex valued hyperspins that can be cast on complex D-vector Hamiltonians. We benchmark the machine against a differential evolution (DE) algorithm on complex D=2 hyperspins up to N=80, showing that the fraction of instances where a lower-energy solution is found grows with system size and coupling density, reaching 92.5% at the largest considered sizes. When the DE finds a lower-energy solution, the machine still reaches a median relative energy deviation that lies between 10−15 and 10−12 while running at substantially lower computational cost. Using the complex nature of the field, we introduce a new dimensional reduction protocol that we name symmetry quenching, which collapses complex variables that map to XY spins onto real Ising spins by switching on the parametric pump. We show on Max-Cut instances with known ground states that symmetry quenching outperforms a fixed-pump Ising machine, reaching exact ground states in the presence of equalization. We scale the system to N=106 hyperspins, or 8×106 dynamical variables, on a Hermitian sparse two-dimensional lattice.
Related
- Hyperspin Altermagnets
- Symmetry-Preserving Local Representation for Short-Range Interaction in Complex Materials
- A Complex Spin-Transition Thermal Hysteresis Unlocked by Two Competing Symmetry-Breakings
- Data analysis of millions of Type IIB flux vacua
- Ab Initio Accuracy Beyond the Cutoff: Distributed Message-Passing Equivariant Attention at Tens-of-Millions-of-Atom Scale
BibTeX
@misc{piacenti2026complex,
title = {{Complex Hyperspin Machine and Symmetry Quenching: Benchmark and scaling up to millions of degrees of freedom}},
author = {Tommaso Piacenti and Marcello Calvanese Strinati and Claudio Conti},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.09324},
eprint = {2611.09324},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.09324},
}
RIS
TY - UNPB
TI - Complex Hyperspin Machine and Symmetry Quenching: Benchmark and scaling up to millions of degrees of freedom
AU - Tommaso Piacenti
AU - Marcello Calvanese Strinati
AU - Claudio Conti
PY - 2026
DA - 2026/11/06
PB - arXiv
DO - 10.48550/arxiv.2611.09324
UR - https://arxiv.org/abs/2611.09324
AB - Driven-dissipative oscillator networks have been proposed to simulate spin models on physical hardware, mostly focusing on systems of binary (Ising) spins, or systems of spin vectors in low dimensions. The equalized hyperspin machine was recently introduced to provide a single platform to simulate general models of N coupled spin vectors with tunable dimension D, realizing dynamical annealing protocols to vary the spin dimensionality in time. These schemes are limited to real spins coupled via real coupling matrices. We propose a generalization of the hyperspin machine that works with complex fields and deals with complex Hermitian coupling matrices, implementing an amplitude equalization scheme. This system, which we name complex hyperspin machine, can work on optimization problems with complex valued hyperspins that can be cast on complex D-vector Hamiltonians. We benchmark the machine against a differential evolution (DE) algorithm on complex D=2 hyperspins up to N=80, showing that the fraction of instances where a lower-energy solution is found grows with system size and coupling density, reaching 92.5% at the largest considered sizes. When the DE finds a lower-energy solution, the machine still reaches a median relative energy deviation that lies between 10^−15 and 10^−12 while running at substantially lower computational cost. Using the complex nature of the field, we introduce a new dimensional reduction protocol that we name symmetry quenching, which collapses complex variables that map to XY spins onto real Ising spins by switching on the parametric pump. We show on Max-Cut instances with known ground states that symmetry quenching outperforms a fixed-pump Ising machine, reaching exact ground states in the presence of equalization. We scale the system to N=10^6 hyperspins, or 8×10^6 dynamical variables, on a Hermitian sparse two-dimensional lattice.
ER -