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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2603.02933 |
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| _version_ | 1866908879859744768 |
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| author | Ekanayake, E. M. Hasantha Venkatakrishnan, Arvind R. Bullo, Francesco Shukla, Nikhil |
| author_facet | Ekanayake, E. M. Hasantha Venkatakrishnan, Arvind R. Bullo, Francesco Shukla, Nikhil |
| contents | The design of nonlinear dynamical systems whose gradient flows minimize the Ising Hamiltonian has emerged as a compelling paradigm for realizing Ising machines, forming the foundation of architectures including coherent Ising machines, simulated bifurcation machines, oscillator-based Ising machines, and dynamical Ising machines. Here, we identify a fundamental structural feature shared by these systems, a functional gap defined by the separation between the destabilization of the trivial state and the stabilization of Ising-encoded states. We demonstrate that this separation creates a finite parameter interval in which convergence to an Ising-encoded solution is no longer functionally guaranteed, and the resulting evolution is dictated by the spectral structure of the Jacobian at bifurcation. Subsequently, by introducing a hybrid dynamical framework that reshapes the bifurcation topology, we establish a principled pathway for modulating this parameter gap. The parameter gap thus emerges as a unifying structural principle for the analysis, design and optimization of analog Ising machines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02933 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mind the Gap: Where Analog Ising Machines Cease to Minimize the Ising Hamiltonian Ekanayake, E. M. Hasantha Venkatakrishnan, Arvind R. Bullo, Francesco Shukla, Nikhil Computational Physics The design of nonlinear dynamical systems whose gradient flows minimize the Ising Hamiltonian has emerged as a compelling paradigm for realizing Ising machines, forming the foundation of architectures including coherent Ising machines, simulated bifurcation machines, oscillator-based Ising machines, and dynamical Ising machines. Here, we identify a fundamental structural feature shared by these systems, a functional gap defined by the separation between the destabilization of the trivial state and the stabilization of Ising-encoded states. We demonstrate that this separation creates a finite parameter interval in which convergence to an Ising-encoded solution is no longer functionally guaranteed, and the resulting evolution is dictated by the spectral structure of the Jacobian at bifurcation. Subsequently, by introducing a hybrid dynamical framework that reshapes the bifurcation topology, we establish a principled pathway for modulating this parameter gap. The parameter gap thus emerges as a unifying structural principle for the analysis, design and optimization of analog Ising machines. |
| title | Mind the Gap: Where Analog Ising Machines Cease to Minimize the Ising Hamiltonian |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2603.02933 |