Original Coverage & Source Attribution: www.nature.com
Mohseni, N., McMahon, P. L. & Byrnes, T. Ising machines as hardware solvers of combinatorial optimization problems. Nat. Rev. Phys. 4, 363–379 (2022).
Lucas, A. Ising formulations of many NP problems. Front. Phys. 2, (2014).
Bybee, C. et al. Efficient optimization with higher-order Ising machines. Nat. Commun. 14, 6033 (2023).
Nikhar, S., Kannan, S., Aadit, N. A., Chowdhury, S. & Camsari, K. Y. All-to-all reconfigurability with sparse and higher-order Ising machines. Nat. Commun. 15, 8977 (2024).
Bhattacharya, T., Hutchinson, G. H., Pedretti, G. & Strukov, D. HO-FPIA: high-order field-programmable Ising arrays with in-memory computing. In 2024 IEEE Computer Society Annual Symposium on VLSI (ISVLSI) 252–259 https://doi.org/10.1109/ISVLSI61997.2024.00054 (2024).
Higgins Hutchinson, G. et al. Compressed high-order Ising machines. IEEE J. Emerg. Sel. Top. Circuits Syst. 16, 577–592 (2026).
Duffee, C. et al. P-dits: probabilistic d-dimensional bits for extended-variable probabilistic computing. Phys. Rev. Appl. 24, 044077 (2025).
Callahan-Coray, K., Lee, K., Jiang, K. & Camsari, K. Y. Restoring sparsity in potts machines via mean-field constraints. npj Unconv. Comput. 3, 50 (2026).
Iyer, D. & Achour, S. Efficient optimization with encoded Ising models. In 2025 IEEE International Symposium on High Performance Computer Architecture (HPCA) 85–98 https://doi.org/10.1109/HPCA61900.2025.00018 (2025).
Garg, C. & Salahuddin, S. Efficient optimization accelerator framework for multi-state spin Ising problems. Nat. Commun. 16, 9601 (2025).
Singh, N. S. et al. Hardware demonstration of feedforward stochastic neural networks with fast MTJ-based p-bits. In 2023 International Electron Devices Meeting (IEDM) 1–4 https://doi.org/10.1109/IEDM45741.2023.10413686 (2023).
Hong, S. Solving inference problems of bayesian networks by probabilistic computing. AIP Adv. 13, 075226 (2023).
Ghantasala, L. A. et al. Improving deep neural network performance through sampling. npj Unconv. Comput. 3, 18 (2026).
Wang, Z., Marandi, A., Wen, K., Byer, R. L. & Yamamoto, Y. Coherent Ising machine based on degenerate optical parametric oscillators. Phys. Rev. A 88, 063853 (2013).
Inagaki, T. et al. A coherent Ising machine for 2000-node optimization problems. Science 354, 603–606 (2016).
McMahon, P. L. et al. A fully programmable 100-spin coherent Ising machine with all-to-all connections. Science 354, 614–617 (2016).
Honjo, T. et al. 100,000-spin coherent Ising machine. Sci. Adv. 7, eabh0952 (2021).
Pierangeli, D., Marcucci, G. & Conti, C. Large-scale photonic Ising machine by spatial light modulation. Phys. Rev. Lett. 122, 213902 (2019).
Roques-Carmes, C. et al. Heuristic recurrent algorithms for photonic Ising machines. Nat. Commun. 11, 249 (2020).
Gao, Y. et al. Photonic Ising machines for combinatorial optimization problems. Appl. Phys. Rev. 11, 041307 (2024).
Kalinin, K. P. et al. Analog optical computer for AI inference and combinatorial optimization. Nature 645, 354–361 (2025).
Veraldi, D. et al. Fully programmable spatial photonic Ising machine by focal plane division. Phys. Rev. Lett. 134, 063802 (2025).
Aadhi, A. et al. Photonic Ising machines toward and beyond a million spins. Preprint at https://doi.org/10.48550/arXiv.2607.13446 (2026).
Wang, T. & Roychowdhury, J. OIM: oscillator-based Ising machines for solving combinatorial optimisation problems. In Unconventional Computation and Natural Computation (eds McQuillan, I. & Seki, S.) 232–256 (Springer, 2019).
Bashar, M. K., Mallick, A. & Shukla, N. Experimental investigation of the dynamics of coupled oscillators as Ising machines. IEEE Access 9, 148184–148190 (2021).
Ahmed, I., Chiu, P.-W., Moy, W. & Kim, C. H. A probabilistic compute fabric based on coupled ring oscillators for solving combinatorial optimization problems. IEEE J. Solid-State Circuits 56, 2870–2880 (2021).
Maher, O. et al. A CMOS-compatible oscillation-based VO2 Ising machine solver. Nat. Commun. 15, 3334 (2024).
Graber, M. & Hofmann, K. An integrated coupled oscillator network to solve optimization problems. Commun. Eng. 3, 116 (2024).
Su, Y., Do, A. T., Kim, T. T.-H. & Kim, B. ROC-spin: a 28 nm 2,000 ring-oscillator-collapse spins for solving combinatorial optimization problems. In 2024 IEEE Asian Solid-State Circuits Conference (a-SSCC) 1–3 https://doi.org/10.1109/A-SSCC60305.2024.10848963 (2024).
Chen, X. et al. Oscillatory neural network-based Ising machine using 2D memristors. ACS Nano 18, 10758–10767 (2024).
Sun, L., Burns, M. X. & Huang, M. C. General oscillator-based Ising-machine models with phase-amplitude dynamics and polynomial interactions. Phys. Rev. Appl. 24, 044035 (2025).
Behera, N. et al. Nanosecond phase ordering in ultra-large spin hall nano-oscillator lattices for unconventional computing. Nat. Nanotechnol. 21, 1105–1112 https://doi.org/10.1038/s41565-026-02216-y (2026).
Ekanayake, E. M. H., Khan, N. & Shukla, N. Configuring oscillator Ising machines as p-bit engines. Commun. Phys. https://doi.org/10.1038/s42005-026-02492-z (2026).
Fahimi, Z., Mahmoodi, M. R., Nili, H., Polishchuk, V. & Strukov, D. B. Combinatorial optimization by weight annealing in memristive hopfield networks. Sci. Rep. 11, 16383 (2021).
Jiang, M., Shan, K., He, C. & Li, C. Efficient combinatorial optimization by quantum-inspired parallel annealing in analogue memristor crossbar. Nat. Commun. 14, 5927 (2023).
Yue, W. et al. A scalable universal Ising machine based on interaction-centric storage and compute-in-memory. Nat. Electron. 7, 904–913 (2024).
Iftakher, M. A. et al. Intrinsic annealing in a hybrid memristor–magnetic tunnel junction Ising machine. Nat. Commun. 17, 5246 (2026).
Aramon, M. et al. Physics-inspired optimization for quadratic unconstrained problems using a digital annealer. Front. Phys. 7, (2019).
Yamaoka, M. et al. A 20k-spin Ising chip to solve combinatorial optimization problems with CMOS annealing. IEEE J. Solid-State Circuits 51, 303–309 (2016).
Goto, H., Tatsumura, K. & Dixon, A. R. Combinatorial optimization by simulating adiabatic bifurcations in nonlinear hamiltonian systems. Sci. Adv. 5, eaav2372 (2019).
Goto, H. et al. High-performance combinatorial optimization based on classical mechanics. Sci. Adv. 7, eabe7953 (2021).
Tatsumura, K., Yamasaki, M. & Goto, H. Scaling out Ising machines using a multi-chip architecture for simulated bifurcation. Nat. Electron. 4, 208–217 (2021).
Kanao, T. & Goto, H. Simulated bifurcation assisted by thermal fluctuation. Commun. Phys. 5, 153 (2022).
Aadit, N. A. et al. Massively parallel probabilistic computing with sparse Ising machines. Nat. Electron. 5, 460–468 (2022).
Chowdhury, S. et al. Pushing the boundary of quantum advantage in hard combinatorial optimization with probabilistic computers. Nat. Commun. 16, 9193 (2025).
Smithson, S. C., Onizawa, N., Meyer, B. H., Gross, W. J. & Hanyu, T. Efficient CMOS invertible logic using stochastic computing. IEEE Trans. Circuits Syst. I Regul. Pap. 66, 2263–2274 (2019).
Singh, N. S. et al. CMOS plus stochastic nanomagnets enabling heterogeneous computers for probabilistic inference and learning. Nat. Commun. 15, 2685 (2024).
Selcuk, K. et al. DAC-free p-bits: asynchronous self-coloring and on-chip annealing. In 2025 IEEE International Electron Devices Meeting (IEDM) 1–4 https://doi.org/10.1109/IEDM50572.2025.11353558 (2025).
Whitehead, W., Nelson, Z., Camsari, K. Y. & Theogarajan, L. CMOS-compatible Ising and potts annealing using single-photon avalanche diodes. Nat. Electron. 6, 1009–1019 (2023).
Borders, W. A. et al. Integer factorization using stochastic magnetic tunnel junctions. Nature 573, 390–393 (2019).
Li, S. et al. An ultra-low power and fast Ising machine using voltage-controlled magnetoresistive random access memory. Preprint at https://doi.org/10.48550/arXiv.2505.19106 (2026).
Yang, S. et al. 250 magnetic tunnel junctions-based probabilistic Ising machine. Nat. Commun. 17, 5368 (2026).
Camsari, K. Y., Faria, R., Sutton, B. M. & Datta, S. Stochastic p-bits for invertible logic. Phys. Rev. X 7, 031014 (2017).
Hayakawa, K. et al. Nanosecond random telegraph noise in in-plane magnetic tunnel junctions. Phys. Rev. Lett. 126, 117202 (2021).
Safranski, C. et al. Demonstration of nanosecond operation in stochastic magnetic tunnel junctions. Nano Lett. 21, 2040–2045 (2021).
Ackley, D. H., Hinton, G. E. & Sejnowski, T. J. A learning algorithm for boltzmann machines. Cognit. Sci. 9, 147–169 (1985).
Singh, N. S. et al. Beyond Ising: mixed continuous optimization with Gaussian probabilistic bits using stochastic MTJs. In 2024 IEEE International Electron Devices Meeting (IEDM) 1–4 https://doi.org/10.1109/IEDM50854.2024.10873478 (2024).
Kalinin, K. P. & Berloff, N. G. Simulating Ising and n-state planar potts models and external fields with nonequilibrium condensates. Phys. Rev. Lett. 121, 235302 (2018).
Chowdhury, S. et al. A full-stack view of probabilistic computing with p-bits: devices, architectures, and algorithms. IEEE J. Explor. Solid-State Comput. Devices Circuits 9, 1–11 (2023).
Weitz, G., Pira, L., Ferrie, C. & Combes, J. Subuniversal variational circuits for combinatorial optimization problems. Phys. Rev. A 112, 032418 (2025).
Abdelrahman, A. S., Chowdhury, S., Morone, F. & Camsari, K. Y. Generalized probabilistic approximate optimization algorithm. Nat. Commun. 17, 498 (2025).
Farhi, E., Goldstone, J., Gutmann, S. & Zhou, L. The quantum approximate optimization algorithm and the sherrington-kirkpatrick model at infinite size. Quantum 6, 759 (2022).
Preskill, J. Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018).
Mohseni, M. et al. How to build a quantum supercomputer: scaling from hundreds to millions of qubits. Preprint at https://doi.org/10.48550/arXiv.2411.10406 (2025).
Kirkpatrick, S., Gelatt, C. D. & Vecchi, M. P. Optimization by simulated annealing. Science 220, 671–680 (1983).
Yamamoto, Y. et al. Coherent Ising machines — optical neural networks operating at the quantum limit. NPJ Quantum Inf. 3, 49 (2017).
Kadowaki, T. & Nishimori, H. Quantum annealing in the transverse Ising model. Phys. Rev. E 58, 5355–5363 (1998).
Suzuki, M. Relationship between d-dimensional quantal spin systems and (d + 1)-dimensional Ising systems: equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56, 1454–1469 (1976).
Camsari, K. Y., Chowdhury, S. & Datta, S. Scalable emulation of sign-problem–free hamiltonians with room-temperature p-bits. Phys. Rev. Appl. 12, 034061 (2019).
Denchev, V. S. et al. What is the computational value of finite-range tunneling? Phys. Rev. X 6, 031015 (2016).
Boixo, S. et al. Evidence for quantum annealing with more than one hundred qubits. Nat. Phys. 10, 218–224 (2014).
Grimaldi, A. et al. Experimental evaluation of simulated quantum annealing with MTJ-augmented p-bits. In 2022 International Electron Devices Meeting (IEDM) 22.4.1–22.4.4 https://doi.org/10.1109/IEDM45625.2022.10019530 (2022).
Onizawa, N., Kubuta, T., Shin, D. & Hanyu, T. Energy-efficient p-bit-based fully-connected quantum-inspired simulated annealer with dual BRAM architecture. IEEE Access 14, 5092–5103 (2026).
Waidyasooriya, H. M. & Hariyama, M. Highly-parallel FPGA accelerator for simulated quantum annealing. IEEE Trans. Emerg. Top. Comput. 9, 2019–2029 (2021).
Raimondo, E. et al. High-performance and reliable probabilistic Ising machine based on simulated quantum annealing. Phys. Rev. X 15, 041001 (2025).
Swendsen, R. H. & Wang, J.-S. Replica Monte Carlo simulation of spin-glasses. Phys. Rev. Lett. 57, 2607–2609 (1986).
Hukushima, K. & Nemoto, K. Exchange Monte Carlo method and application to spin glass simulations. J. Phys. Soc. Jpn. 65, 1604–1608 (1996).
Marinari, E. & Parisi, G. Simulated tempering: a new Monte Carlo scheme. EPL 19, 451–458 (1992).
Earl, D. J. & Deem, M. W. Parallel tempering: theory, applications, and new perspectives. Phys. Chem. Chem. Phys. 7, 3910–3916 (2005).
Aadit, N. A., Mohseni, M. & Camsari, K. Y. Accelerating adaptive parallel tempering with FPGA-based p-bits. In 2023 IEEE Symposium on VLSI Technology And Circuits (VLSI technology and circuits) 1–2 https://doi.org/10.23919/VLSITechnologyandCir57934.2023.10185207 (2023).
Nakayama, H., Koyama, J., Yoneoka, N. & Miyazawa, T. Description: Third Generation Digital Annealer Technology (Fujitsu Ltd., 2021).
Zhang, Y. et al. A parallel tempering processing architecture with multi-spin update for fully-connected Ising models. In 2024 Design, Automation & Test In Europe Conference & Exhibition (DATE) 1–6 https://doi.org/10.23919/DATE58400.2024.10546862 (2024).
Zhu, Z., Ochoa, A. J. & Katzgraber, H. G. Efficient cluster algorithm for spin glasses in any space dimension. Phys. Rev. Lett. 115, 077201 (2015).
Zhang, X. et al. Parallel tempering-inspired distributed binary optimization with in-memory computing. Phys. Rev. Appl. 23, 034031 (2025).
Sajeeb, M. M. H. et al. Probabilistic computers for MIMO detection: from sparsification to 2D parallel tempering. Preprint at https://doi.org/10.48550/arXiv.2601.09037 (2026).
Zhu, R. et al. A fully parallel densely connected probabilistic Ising machine with inertia for real-time applications. Preprint at https://doi.org/10.48550/arXiv.2604.17109 (2026).
Hopfield, J. J. & Tank, D. W. ‘Neural’ computation of decisions in optimization problems. Biol. Cybern. 52, 141–152 (1985).
Sajeeb, M. M. H. et al. Scalable connectivity for Ising machines: dense to sparse. Phys. Rev. Appl. 24, 014005 (2025).
Delacour, C. Self-adaptive Ising machines for constrained optimization. In 2025 Design, Automation & Test In Europe Conference (DATE) 1–7 https://doi.org/10.23919/DATE64628.2025.10992982 (2025).
Lee, J., Miller, B. T., Damjanović, A. & Brooks, B. R. Enhancing constant-pH simulation in explicit solvent with a two-dimensional replica exchange method. J. Chem. Theory Comput. 11, 2560–2574 (2015).
Delacour, C., Sajeeb, M. M. H., P. Hespanha, J. & Camsari, K. Y. Two-dimensional parallel tempering for constrained optimization. Phys. Rev. E 112, L023301 https://doi.org/10.1103/mr2n-qqrb (2025).
Grimaldi, A. et al. Constrained parallel tempering in traveling-salesman problems with circular neighborhoods. Phys. Rev. Appl. 25, 024023 (2026).
Yamamoto, D. Correlated cluster mean-field theory for spin systems. Phys. Rev. B 79, 144427 (2009).
Xing, E. P., Jordan, M. I. & Russell, S. A generalized mean field algorithm for variational inference in exponential families. In Proc. Nineteenth Conference on Uncertainty in Artificial Intelligence 583–591 (Morgan Kaufmann Publishers, 2002).
Huang, Y. et al. GPipe: efficient training of giant neural networks using pipeline parallelism. In Proc. 33rd International Conference on Neural Information Processing Systems 10, 103–112 (Curran Assoc. Inc, 2019).
Narayanan, D. et al. PipeDream: generalized pipeline parallelism for DNN training. In Proc. 27th ACM Symposium on Operating Systems Principles 1–15 https://doi.org/10.1145/3341301.3359646 (2019).
Qi, P., Wan, X., Huang, G. & Lin, M. Zero bubble (almost) pipeline parallelism. In The Twelfth International Conference on Learning Representations (ICLR) (2024).
Shoeybi, M. et al. Megatron-LM: training multi-billion parameter language models using model parallelism. Preprint at https://doi.org/10.48550/arXiv.1909.08053 (2019).
Tanaka, M., Taura, K., Hanawa, T. & Torisawa, K. Automatic graph partitioning for very large-scale deep learning. In 2021 IEEE International Parallel and Distributed Processing Symposium (IPDPS) 1004–1013 https://doi.org/10.1109/IPDPS49936.2021.00109 (IEEE, 2021).
Zhou, L., Wang, S.-T., Choi, S., Pichler, H. & Lukin, M. D. Quantum approximate optimization algorithm: performance, mechanism, and implementation on near-term devices. Phys. Rev. X 10, 021067 (2020).
Basso, J., Farhi, E., Marwaha, K., Villalonga, B. & Zhou, L. The quantum approximate optimization algorithm at high depth for MaxCut on large-girth regular graphs and the Sherrington-Kirkpatrick model. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022) (eds Le Gall, F. & Morimae, T.) vol. 232, 7:1–7:21 (Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2022).
Sakai, R., Matsuyama, H., Tam, W.-H. & Yamashiro, Y. Transferring linearly fixed QAOA angles: performance and real device results. Preprint at https://doi.org/10.48550/arXiv.2504.12632 (2025).
Cerezo, M. et al. Variational quantum algorithms. Nat. Rev. Phys. 3, 625–644 (2021).
Morone, F., Kent, A. D. & Sels, D. Variational iterative rotation algorithm: combinatorial optimization with classical kicked tops. Preprint at https://doi.org/10.48550/arXiv.2604.01512 (2026).
Alsawidan, Z. et al. Probabilistic approximate optimization using single-photon avalanche diode arrays. Preprint at https://doi.org/10.48550/arXiv.2602.13943 (2026).
Adame, J. I. & McMahon, P. L. Inhomogeneous driving in quantum annealers can result in orders-of-magnitude improvements in performance. Quantum Sci. Technol. 5, 035011 (2020).
Mohseni, M. et al. Nonequilibrium Monte Carlo for unfreezing variables in hard combinatorial optimization. Preprint at https://doi.org/10.48550/arXiv.2111.13628 (2021).
Carleo, G. & Troyer, M. Solving the quantum many-body problem with artificial neural networks. Science 355, 602–606 (2017).
Fabiani, G. & Mentink, J. H. Investigating ultrafast quantum magnetism with machine learning. SciPost Phys. 7, 004 (2019).
Schmitt, M. & Heyl, M. Quantum many-body dynamics in two dimensions with artificial neural networks. Phys. Rev. Lett. 125, 100503 (2020).
Vicentini, F. et al. NetKet 3: machine learning toolbox for many-body quantum systems. SciPost Phys. Codebases 7 https://doi.org/10.21468/SciPostPhysCodeb.7 (2022).
Schmitt, M. & Reh, M. jVMC: versatile and performant variational Monte Carlo leveraging automated differentiation and GPU acceleration. SciPost Phys. Codebases 2 https://doi.org/10.21468/SciPostPhysCodeb.2 (2022).
Chen, A. & Heyl, M. Empowering deep neural quantum states through efficient optimization. Nat. Phys. 20, 1476–1481 (2024).
Moss, M. S., Wiersema, R., Hibat-Allah, M., Carrasquilla, J. & Melko, R. G. Leveraging recurrence in neural network wavefunctions for large-scale simulations of Heisenberg antiferromagnets on the square lattice. Phys. Rev. B 112, 134450 (2025).
Chowdhury, S., Pieterse, J., Aadit, N. A., Mentink, J. H. & Camsari, K. Y. Probabilistic computers for neural quantum states. Preprint at https://doi.org/10.48550/arXiv.2512.24558 (2025).
Chowdhury, S., Çamsari, K. Y. & Datta, S. Emulating quantum circuits with generalized Ising machines. IEEE Access 11, 116944–116955 (2023).
Troyer, M. et al. Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations. Phys. Rev. Lett. 94, 170201 (2005).
Hangleiter, D., Roth, I., Nagaj, D. & Eisert, J. Easing the Monte Carlo sign problem. Sci. Adv. 6, eabb8341 (2020).
Marvian, M., Lidar, D. A. & Hen, I. On the computational complexity of curing non-stoquastic Hamiltonians. Nat. Commun. 10, 1571 (2019).
Jung, G. et al. Roadmap on machine learning glassy dynamics. Nat. Rev. Phys. 7, 91–104 (2025).
Schuetz, M. J. A., Brubaker, J. K. & Katzgraber, H. G. Combinatorial optimization with physics-inspired graph neural networks. Nat. Mach. Intell. 4, 367–377 (2022).
Williams, R. J. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Mach. Learn. 8, 229–256 (1992).
Bojesen, T. A. Policy-guided Monte Carlo: reinforcement-learning Markov chain dynamics. Phys. Rev. E 98, 063303 (2018).
Wu, D., Wang, L. & Zhang, P. Solving statistical mechanics using variational autoregressive networks. Phys. Rev. Lett. 122, 080602 (2019).
Nicoli, K. A. et al. Asymptotically unbiased estimation of physical observables with neural samplers. Phys. Rev. E 101, 023304 (2020).
Sanokowski, S., Hochreiter, S. & Lehner, S. A diffusion model framework for unsupervised neural combinatorial optimization. Preprint at https://doi.org/10.48550/arXiv.2406.01661 (2025).
Sanokowski, S. et al. Scalable discrete diffusion samplers: combinatorial optimization and statistical physics. Preprint at https://doi.org/10.48550/arXiv.2502.08696 (2025).
Hibat-Allah, M., Inack, E. M., Wiersema, R., Melko, R. G. & Carrasquilla, J. Variational neural annealing. Nat. Mach. Intell. 3, 952–961 (2021).
Ma, Q., Ma, Z., Xu, J., Zhang, H. & Gao, M. Message passing variational autoregressive network for solving intractable Ising models. Commun. Phys. 7, 236 (2024).
Zhang, Y.-H. & Ventra, M. D. A generative neural annealer for black-box combinatorial optimization. Preprint at https://doi.org/10.48550/arXiv.2505.09742 (2025).
Bunaiyan, S., Delacour, C., Chowdhury, S., Lee, K. & Camsari, K. Y. IsingFormer: augmenting parallel tempering with learned proposals. Preprint at https://doi.org/10.48550/arXiv.2509.23043 (2025).
Invernizzi, M., Krämer, A., Clementi, C. & Noé, F. Skipping the replica exchange ladder with normalizing flows. J. Phys. Chem. Lett. 13, 11643–11649 (2022).
Zhang, L. et al. Accelerated parallel tempering via neural transports. Preprint at https://doi.org/10.48550/arXiv.2502.10328 (2025).
Del Bono, L. M., Ricci-Tersenghi, F. & Zamponi, F. Demonstrating real advantage of machine-learning-enhanced Monte Carlo for combinatorial optimization. Proc. Natl Acad. Sci. USA 123, e2534768123 (2026).
Lee, K. et al. Stochastic sparse attention for memory-bound inference. In Proc. 43rd International Conference on Machine Learning (ICML) (2026).
Liu, Y. et al. Energy-efficient parallel Ising SoftMax engine for transformer attention based on asynchronous SOT-p-bits. In IEEE Electron Device Letters 1–1 https://doi.org/10.1109/LED.2026.3691358 (2026).
