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1. Ising-FPGA: A Spintronics-based Reconfigurable Ising Model Solver

   https://doi.org/10.1145/3411511  

   Mondal, Ankit; Srivastava, Ankur (January 2021, ACM Transactions on Design Automation of Electronic Systems)

   null (Ed.)

   The Ising model has been explored as a framework for modeling NP-hard problems, with several diverse systems proposed to solve it. The Magnetic Tunnel Junction– (MTJ) based Magnetic RAM is capable of replacing CMOS in memory chips. In this article, we propose the use of MTJs for representing the units of an Ising model and leveraging its intrinsic physics for finding the ground state of the system through annealing. We design the structure of a basic MTJ-based Ising cell capable of performing the functions essential to an Ising solver. The hardware overhead of the Ising model is analyzed, and a technique to use the basic Ising cell for scaling to large problems is described. We then go on to propose Ising-FPGA, a parallel and reconfigurable architecture that can be used to map a large class of NP-hard problems, and show how a standard Place and Route tool can be utilized to program the Ising-FPGA. The effects of this hardware platform on our proposed design are characterized and methods to overcome these effects are prescribed. We discuss how three representative NP-hard problems can be mapped to the Ising model. Further, we suggest ways to simplify these problems to reduce the use of hardware and analyze the impact of these simplifications on the quality of solutions. Simulation results show the effectiveness of MTJs as Ising units by producing solutions close/comparable to the optimum and demonstrate that our design methodology holds the capability to account for the effects of the hardware. 

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2. Testing Ising Models

   Daskalakis, Constantinos; Dikkala, Nishanth; Kamath, Gautam (January 2018, Proceedings of the annual ACM-SIAM Symposium on Discrete Algorithms)

   Given samples from an unknown multivariate distribution p, is it possible to distinguish whether p is the product of its marginals versus p being far from every product distribution? Similarly, is it possible to distinguish whether p equals a given distribution q versus p and q being far from each other? These problems of testing independence and goodness-of-fit have received enormous attention in statistics, information theory, and theoretical computer science, with sample-optimal algorithms known in several interesting regimes of parameters [BFF+01, Pan08, VV17, ADK15, DK16]. Unfortunately, it has also been understood that these problems become intractable in large dimensions, necessitating exponential sample complexity. Motivated by the exponential lower bounds for general distributions as well as the ubiquity of Markov Random Fields (MRFs) in the modeling of high-dimensional distributions, we initiate the study of distribution testing on structured multivariate distributions, and in particular the prototypical example of MRFs: the Ising Model. We demonstrate that, in this structured setting, we can avoid the curse of dimensionality, obtaining sample and time efficient testers for independence and goodness-of-fit. One of the key technical challenges we face along the way is bounding the variance of functions of the Ising model. 

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3. Nonreciprocal Ising Model

   https://doi.org/10.1103/PhysRevLett.134.117103  

   Avni, Yael; Fruchart, Michel; Martin, David; Seara, Daniel; Vitelli, Vincenzo (March 2025, Physical Review Letters)
4. Bistable Latch Ising Machines

   https://doi.org/10.1007/978-3-030-87993-8_9  

   Roychowdhury, Jaijeet (October 2021, Unconventional Computation and Natural Computation: 19th International Conference, UCNC 2021, Espoo, Finland, October 18–22, 2021, Proceedings)

   Ising machines have been attracting attention due to their ability to use mixed discrete/continuous mechanisms to solve difficult combinatorial optimization problems. We present BLIM, a novel Ising machine scheme that uses latches (bistable elements) with controllable gains as Ising spins. We show that networks of coupled latches have a Lyapunov or “energy” function that matches the Ising Hamiltonian in discrete operation, enabling them to function as Ising machines. This result is established in a general coupled-element Ising machine framework that is not limited to BLIM. Operating the latches periodically in analog/continuous mode, during which bistability is removed, helps the system traverse to better minima. CMOS realizations of BLIM have desirable practical features; implementation in other physical domains is an intriguing possibility. 

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5. Measurement-Altered Ising Quantum Criticality

   https://doi.org/10.1103/PhysRevX.13.041042  

   Murciano, Sara; Sala, Pablo; Liu, Yue; Mong, Roger_S K; Alicea, Jason (December 2023, Physical Review X)