Continuous approximation of the Ising Hamiltonian: Exact ground states and applications to fidelity assessment in Ising machines

2024/11/29 by Amirhossein Rezaei, Mahmood Hasani, Rezaei, Amirhossein +5 · 1 voice
Physics and Astronomy · Computer Science · #Quantum many-body systems #Quantum Computing Algorithms and Architecture #Opinion Dynamics and Social Influence

paper · doi:10.1103/w88d-7rqz

openalex created_date 2024/12/05 · openalex publication_date 2025/07/14 · openalex updated_date 2026/07/28

Abstract

In this study, we present an alternative analytical approach to solving large-scale Ising problems by reformulating the discrete Ising Hamiltonian into a continuous framework. This transformation enables us to derive exact solutions for a nontrivial class of fully connected Ising models. To validate our method, we conducted numerical experiments comparing our analytical solutions with those obtained from a quantum-inspired Ising algorithm and a quantum Ising machine. The results demonstrate that the quantum-inspired algorithm and brute-force method successfully align with our solutions, while the quantum Ising machine exhibits notable deviations. Our method offers promising avenues for analytically solving diverse Ising problem instances, while the class of Ising problems addressed here provides a robust framework for assessing the fidelity of Ising machines.

Citations

• Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm
• Quantum critical dynamics in a 5,000-qubit programmable spin glass

Discussions

• When I first asked this question, I hoped to find examples of real-world systems described by the interaction matrix $$ J_{ij} = \frac{(i^d + j^d)}{N^d} (1 - \delta_{ij}), $$ where $d$ can be any real [stackexchange, 0 points]

Related

• A quantum algorithm for additive approximation of Ising partition functions
• Towards quantum simulation of spin systems using continuous variable quantum devices
• Certifying and learning quantum Ising Hamiltonians
• Quantum-Inspired Ising Machines for Quantum Chemistry Calculations
• On the mathematical structure of quantum models of computation based on Hamiltonian minimisation