Han, S. et al. EIE: efficient inference engine on compressed deep neural network. ACM SIGARCH Comput. Archit. News 44, 243–254 (2016).
Google Scholar
Chen, Y.-H., Krishna, T., Emer, J. S. & Sze, V. Eyeriss: an energy-efficient reconfigurable accelerator for deep convolutional neural networks. IEEE J. Solid State Circuits 52, 127–138 (2016).
Google Scholar
Shao, Y. S. et al. Simba: Scaling deep-learning inference with multi-chip-module-based architecture. In Proc. 52nd Annual IEEE/ACM International Symposium on Microarchitecture 14–27 (ACM, 2019).
Reuther, A. et al. Survey of machine learning accelerators. In Proc. 2020 IEEE High Performance Extreme Computing Conference (HPEC) 1–12 (IEEE, 2020).
Shun, J. & Blelloch, G. E. Ligra: a lightweight graph processing framework for shared memory. In Proc. 18th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming 135–146 (ACM, 2013).
Abadal, S., Jain, A., Guirado, R., López-Alonso, J. & Alarcón, E. Computing graph neural networks: a survey from algorithms to accelerators. ACM Comput. Surv. 54, 1–38 (2021).
Google Scholar
Low, Y. et al. GraphLab: a new framework for parallel machine learning. In Proc. 26th Conference on Uncertainty in Artificial Intelligence 340–349 (ACM, 2014).
Mohseni, N., McMahon, P. L. & Byrnes, T. Ising machines as hardware solvers of combinatorial optimization problems. Nat. Rev. Phys. 4, 363–379 (2022).
Google Scholar
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 (2015).
Tatsumura, K., Yamasaki, M. & Goto, H. Scaling out Ising machines using a multi-chip architecture for simulated bifurcation. Nat. Electron. 4, 208–217 (2021).
Google Scholar
Lo, H., Moy, W., Yu, H., Sapatnekar, S. & Kim, C. H. An Ising solver chip based on coupled ring oscillators with a 48-node all-to-all connected array architecture. Nat. Electron. 6, 771–778 (2023).
Google Scholar
Shalf, J. The future of computing beyond Moore’s law. Philos. Trans. R. Soc. A 378, 20190061 (2020).
Google Scholar
Horowitz, M. 1.1 Computing’s energy problem (and what we can do about it). In Proc. 2014 IEEE International Solid-state Circuits Conference Digest of Technical Papers (ISSCC) 10–14 (IEEE, 2014).
Jouppi, N. P. et al. Ten lessons from three generations shaped Google’s TPUv4i: industrial product. In Proc. 2021 ACM/IEEE 48th Annual International Symposium on Computer Architecture (ISCA) 1–14 (IEEE, 2021).
Ryckaert, J. & Samavedam, S. B. The CMOS 2.0 revolution. Nat. Rev. Electr. Eng. 1, 139–140 (2024).
Google Scholar
Hennessy, J. L. & Patterson, D. A. Computer Architecture: A Quantitative Approach (Elsevier, 2011).
Muralidhar, R., Borovica-Gajic, R. & Buyya, R. Energy efficient computing systems: architectures, abstractions and modeling to techniques and standards. ACM Comput. Surv. 54, 1–37 (2022).
Google Scholar
Hill, M. D. & Reddi, V. J. Accelerator-level parallelism. Commun. ACM 64, 36–38 (2021).
Google Scholar
Zha, D. et al. Data-centric artificial intelligence: a survey. ACM Comput. Surv. 57, 129 (2023).
Bhatt, N. et al. A data-centric approach to improve performance of deep learning models. Sci. Rep. 14, 22329 (2024).
Google Scholar
Dally, W. J., Turakhia, Y. & Han, S. Domain-specific hardware accelerators. Commun. ACM 63, 48–57 (2020).
Google Scholar
Sebastian, A., Le Gallo, M., Khaddam-Aljameh, R. & Eleftheriou, E. Memory devices and applications for in-memory computing. Nat. Nanotechnol. 15, 529–544 (2020).
Google Scholar
Wright, L. G. et al. Deep physical neural networks trained with backpropagation. Nature 601, 549–555 (2022).
Google Scholar
Grollier, J. et al. Neuromorphic spintronics. Nat. Electron. 3, 360–370 (2020).
Google Scholar
Finocchio, G. et al. The promise of spintronics for unconventional computing. J. Magn. Magn. Mater. 521, 167506 (2021).
Google Scholar
Watanabe, K., Jinnai, B., Fukami, S., Sato, H. & Ohno, H. Shape anisotropy revisited in single-digit nanometer magnetic tunnel junctions. Nat. Commun. 9, 663 (2018).
Google Scholar
Behera, N. et al. Ultra-low current 10 nm spin Hall nano-oscillators. Adv. Mater. 36, 2305002 (2024).
Google Scholar
Jangra, P. & Duhan, M. In-memory computing: characteristics, spintronics, and neural network applications insights. Multiscale Multidiscip. Model. Exp. Des. 7, 5005–5029 (2024).
Google Scholar
Borders, W. A. et al. Measurement-driven neural-network training for integrated magnetic tunnel junction arrays. Phys. Rev. Appl. 21, 054028 (2024).
Google Scholar
Jung, S. et al. A crossbar array of magnetoresistive memory devices for in-memory computing. Nature 601, 211–216 (2022).
Google Scholar
Guo, K. et al. Neural network accelerator comparison. NICSEFC (accessed 2 September 2025); https://nicsefc.ee.tsinghua.edu.cn/projects/neural-network-accelerator/.
Roy, K. et al. Spintronic neural systems. Nat. Rev. Electr. Eng. 1, 714–729 (2024).
Google Scholar
Rodrigues, D. R. et al. Spintronic Hodgkin-Huxley-analogue neuron implemented with a single magnetic tunnel junction. Phys. Rev. Appl. 19, 064010 (2023).
Google Scholar
Chakraborty, I. et al. Resistive crossbars as approximate hardware building blocks for machine learning: opportunities and challenges. Proc. IEEE 108, 2276–2310 (2020).
Google Scholar
Ross, A. et al. Multilayer spintronic neural networks with radiofrequency connections. Nat. Nanotechnol. 18, 1273–1280 (2023).
Google Scholar
Zeng, K. et al. Radio-frequency-modulated artificial synapses based on magnetic tunnel junctions with perpendicular magnetic anisotropy. Phys. Rev. Appl. 21, 014020 (2024).
Google Scholar
Tulapurkar, A. A. et al. Spin-torque diode effect in magnetic tunnel junctions. Nature 438, 339–342 (2005).
Google Scholar
Leroux, N. et al. Convolutional neural networks with radio-frequency spintronic nano-devices. Neuromorphic Comput. Eng. 2, 034002 (2022).
Google Scholar
Cai, J. et al. Sparse neuromorphic computing based on spin-torque diodes. Appl. Phys. Lett. 114, 192402 (2019).
Google Scholar
Böhnert, T. et al. Weighted spin torque nano-oscillator system for neuromorphic computing. Commun. Eng. 2, 65 (2023).
Google Scholar
Kariyappa, S. et al. Noise-resilient DNN: tolerating noise in PCM-based AI accelerators via noise-aware training. IEEE Trans. Electron Devices 68, 4356–4362 (2021).
Google Scholar
Buckley, S. M., Tait, A. N., McCaughan, A. N. & Shastri, B. J. Photonic online learning: a perspective. Nanophotonics 12, 833–845 (2023).
Google Scholar
Lv, C. et al. Towards biologically plausible computing: a comprehensive comparison. Preprint at https://arxiv.org/abs/2406.16062 (2024).
Mazza, L. et al. Computing with injection-locked spintronic diodes. Phys. Rev. Appl. 17, 014045 (2022).
Google Scholar
Goto, M. et al. Uncooled sub-GHz spin bolometer driven by auto-oscillation. Nat. Commun. 12, 536 (2021).
Google Scholar
Fang, B. et al. Giant spin-torque diode sensitivity in the absence of bias magnetic field. Nat. Commun. 7, 11259 (2016).
Google Scholar
Finocchio, G. et al. Perspectives on spintronic diodes. Appl. Phys. Lett. 118, 160502 (2021).
Google Scholar
Jiang, S. et al. Spin-torque nano-oscillators and their applications. Appl. Phys. Rev. 11, 041309 (2024).
Google Scholar
Goto, M. et al. Microwave amplification in a magnetic tunnel junction induced by heat-to-spin conversion at the nanoscale. Nat. Nanotechnol. 14, 40–43 (2019).
Google Scholar
Zhu, K. et al. Nonlinear amplification of microwave signals in spin-torque oscillators. Nat. Commun. 14, 2183 (2023).
Google Scholar
Behera, A. P. et al. Exploring the boundaries of on-device inference: when tiny falls short, go hierarchical. IEEE Internet Things J. 12, 37456–37470 (2024).
Google Scholar
Camsari, K. Y., Faria, R., Sutton, B. M. & Datta, S. Stochastic p-bits for invertible logic. Phys. Rev. X 7, 031014 (2017).
Borders, W. A. et al. Integer factorization using stochastic magnetic tunnel junctions. Nature 573, 390–393 (2019).
Google Scholar
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).
Google Scholar
Chowdhury, S., Camsari, K. Y. & Datta, S. Emulating quantum circuits with generalized Ising machines. IEEE Access 11, 116944–116955 (2023).
Google Scholar
Singh, N. S. et al. CMOS plus stochastic nanomagnets enabling heterogeneous computers for probabilistic inference and learning. Nat. Commun. 15, 2685 (2024).
Google Scholar
Sutton, B., Camsari, K. Y., Behin-Aein, B. & Datta, S. Intrinsic optimization using stochastic nanomagnets. Sci. Rep. 7, 44370 (2017).
Google Scholar
Lv, Y., Bloom, R. P. & Wang, J.-P. Experimental demonstration of probabilistic spin logic by magnetic tunnel junctions. IEEE Magn. Lett. 10, 4510905 (2019).
Google Scholar
Yin, J. et al. Scalable Ising computer based on ultra-fast field-free spin orbit torque stochastic device with extreme 1-bit quantization. In Proc. 2022 International Electron Devices Meeting (IEDM) 36.1.1–36.1.4 (IEEE, 2022).
Si, J. et al. Energy-efficient superparamagnetic Ising machine and its application to traveling salesman problems. Nat. Commun. 15, 3457 (2024).
Google Scholar
Mizrahi, A. et al. Neural-like computing with populations of superparamagnetic basis functions. Nat. Commun. 9, 1533 (2018).
Google Scholar
Kaiser, J. et al. Hardware-aware in situ learning based on stochastic magnetic tunnel junctions. Phys. Rev. Appl. 17, 014016 (2022).
Google Scholar
Li, X. et al. Restricted Boltzmann machines implemented by spin–orbit torque magnetic tunnel junctions. Nano Lett. 24, 5420–5428 (2024).
Google Scholar
Singh, N. S. et al. Hardware demonstration of feedforward stochastic neural networks with fast MTJ-based p-bits. In Proc. 2023 International Electron Devices Meeting (IEDM) 12.1.1–12.1.4 (IEEE, 2023).
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).
Google Scholar
Grimaldi, A. et al. Experimental evaluation of simulated quantum annealing with MTJ-augmented p-bits. In Proc. 2022 International Electron Devices Meeting (IEDM) 22.4.1–22.4.4 (IEEE, 2022).
Grimaldi, A. et al. Spintronics-compatible approach to solving maximum-satisfiability problems with probabilistic computing, invertible logic, and parallel tempering. Phys. Rev. Appl. 17, 024052 (2022).
Google Scholar
Onizawa, N. & Hanyu, T. Enhanced convergence in p-bit based simulated annealing with partial deactivation for large-scale combinatorial optimization problems. Sci. Rep. 14, 1339 (2024).
Google Scholar
Aadit, N. A., Mohseni, M. & Camsari, K. Y. Accelerating adaptive parallel tempering with FPGA-based p-bits. In Proc. 2023 IEEE Symposium on VLSI Technology and Circuits 1–2 (IEEE, 2023).
Niazi, S. et al. Training deep Boltzmann networks with sparse Ising machines. Nat. Electron. 7, 610–619 (2024).
Google Scholar
Ostwal, V. & Appenzeller, J. Spin-orbit torque-controlled magnetic tunnel junction with low thermal stability for tunable random number generation. IEEE Magn. Lett. 10, 4503305 (2019).
Google Scholar
Fukushima, A. et al. Spin dice: a scalable truly random number generator based on spintronics. Appl. Phys. Express 7, 083001 (2014).
Google Scholar
Shao, Y. et al. Implementation of artificial neural networks using magnetoresistive random-access memory-based stochastic computing units. IEEE Magn. Lett. 12, 4501005 (2021).
Google Scholar
Rehm, L. et al. Stochastic magnetic actuated random transducer devices based on perpendicular magnetic tunnel junctions. Phys. Rev. Appl. 19, 024035 (2023).
Google Scholar
Ren, R. et al. Initialization-free and magnetic field-free spin–orbit p-bits with backhopping-like magnetization switching for probabilistic applications. Nano Lett. 24, 10072–10080 (2024).
Google Scholar
Liu, S. et al. Random bitstream generation using voltage-controlled magnetic anisotropy and spin orbit torque magnetic tunnel junctions. IEEE J. Explor. Solid State Comput. Devices Circuits 8, 194–202 (2022).
Google Scholar
Bandyopadhyay, S. Straintronics: digital and analog electronics with strain-switched nanomagnets. IEEE Open J. Nanotechnol. 1, 57–64 (2020).
Google Scholar
Phan, N.-T. et al. Unbiased random bitstream generation using injection-locked spin-torque nano-oscillators. Phys. Rev. Appl. 21, 034063 (2024).
Google Scholar
Debashis, P., Faria, R., Camsari, K. Y., Datta, S. & Chen, Z. Correlated fluctuations in spin orbit torque coupled perpendicular nanomagnets. Phys. Rev. B 101, 094405 (2020).
Google Scholar
Talatchian, P. et al. Mutual control of stochastic switching for two electrically coupled superparamagnetic tunnel junctions. Phys. Rev. B 104, 054427 (2021).
Google Scholar
Schnitzspan, L., Kläui, M. & Jakob, G. Electrical coupling of superparamagnetic tunnel junctions mediated by spin-transfer-torques. Appl. Phys. Lett. 123, 232403 (2023).
Google Scholar
Gibeault, S. et al. Programmable electrical coupling between stochastic magnetic tunnel junctions. Phys. Rev. Appl. 21, 034064 (2024).
Google Scholar
Liu, Y. et al. Probabilistic circuit implementation based on p-bits using the intrinsic random property of RRAM and p-bit multiplexing strategy. Micromachines 13, 924 (2022).
Google Scholar
Woo, K. S. et al. Probabilistic computing using Cu0.1Te0.9/HfO2/Pt diffusive memristors. Nat. Commun. 13, 5762 (2022).
Google Scholar
Park, T. J. et al. Efficient probabilistic computing with stochastic perovskite nickelates. Nano Lett. 22, 8654–8661 (2022).
Google Scholar
Luo, S., He, Y., Cai, B., Gong, X. & Liang, G. Probabilistic-bits based on ferroelectric field-effect transistors for probabilistic computing. IEEE Electron Device Lett. 44, 1356–1359 (2023).
Google Scholar
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).
Google Scholar
Patel, S. et al. PASS: an asynchronous probabilistic processor for next generation intelligence. Preprint at https://arxiv.org/abs/2409.10325 (2024).
Wu, J., Sun, H. & Zhou, G. True random number generator based on chaotic oscillation of a tunable double-well MEMS resonator. Small 20, 2403755 (2024).
Google Scholar
Hayakawa, K. et al. Nanosecond random telegraph noise in in-plane magnetic tunnel junctions. Phys. Rev. Lett. 126, 117202 (2021).
Google Scholar
Safranski, C. et al. Demonstration of nanosecond operation in stochastic magnetic tunnel junctions. Nano Lett. 21, 2040–2045 (2021).
Google Scholar
Schnitzspan, L., Kläui, M. & Jakob, G. Nanosecond true-random-number generation with superparamagnetic tunnel junctions: identification of Joule heating and spin-transfer-torque effects. Phys. Rev. Appl. 20, 024002 (2023).
Google Scholar
Kanai, S., Hayakawa, K., Ohno, H. & Fukami, S. Theory of relaxation time of stochastic nanomagnets. Phys. Rev. B 103, 094423 (2021).
Google Scholar
Hassan, O., Datta, S. & Camsari, K. Y. Quantitative evaluation of hardware binary stochastic neurons. Phys. Rev. Appl. 15, 064046 (2021).
Google Scholar
Sutton, B. et al. Autonomous probabilistic coprocessing with petaflips per second. IEEE Access 8, 157238–157252 (2020).
Google Scholar
Cheemalavagu, S., Korkmaz, P., Palem, K. V., Akgul, B. E. & Chakrapani, L. N. A probabilistic CMOS switch and its realization by exploiting noise. In Proc. IFIP International Conference on VLSI 535–541 (IFIP, 2005).
Camsari, K. Y., Salahuddin, S. & Datta, S. Implementing p-bits with embedded MTJ. IEEE Electron Device Lett. 38, 1767–1770 (2017).
Google Scholar
Camsari, K. Y., Torunbalci, M. M., Borders, W. A., Ohno, H. & Fukami, S. Double-free-layer magnetic tunnel junctions for probabilistic bits. Phys. Rev. Appl. 15, 044049 (2021).
Google Scholar
Ota, R. et al. Voltage-insensitive stochastic magnetic tunnel junctions with double free layers. Appl. Phys. Lett. 125, 022406 (2024).
Google Scholar
Selcuk, K. et al. Double-free-layer stochastic magnetic tunnel junctions with synthetic antiferromagnets. Phys. Rev. Appl. 21, 054002 (2024).
Google Scholar
Dieny, B. et al. Impact of external magnetic fields on STT-MRAM: an application note. IEEE Electron Devices Mag. 2, 52–59 (2024).
Google Scholar
Kobayashi, K. et al. External-field-robust stochastic magnetic tunnel junctions using a free layer with synthetic antiferromagnetic coupling. Phys. Rev. Appl. 18, 054085 (2022).
Google Scholar
Sun, J. Z. et al. Stochastic magnetic tunnel junction with easy-plane dominant anisotropy. Phys. Rev. B 107, 184433 (2023).
Google Scholar
Sun, J. Z. et al. Easy-plane dominant stochastic magnetic tunnel junction with synthetic antiferromagnetic layers. Phys. Rev. B 108, 064418 (2023).
Google Scholar
Kaneko, H. et al. Temperature dependence of the properties of stochastic magnetic tunnel junction with perpendicular magnetization. Appl. Phys. Express 17, 053001 (2024).
Google Scholar
Elyasi, M., Kanai, S., Ohno, H., Fukami, S. & Bauer, G. E. W. Effect of nonlinear magnon interactions on stochastic magnetization switching. Phys. Rev. B 110, 094433 (2024).
Google Scholar
French, R. M. Catastrophic forgetting in connectionist networks. Trends Cogn. Sci. 3, 128–135 (1999).
Google Scholar
Nakajima, K. & Fischer, I. Reservoir Computing (Springer, 2021).
Jaeger, H. The ‘Echo State’ Approach to Analysing and Training Recurrent Neural Networks — With an Erratum Note. GMD Report 148 (German National Research Institute for Computer Science, 2001).
Maass, W., Natschläger, T. & Markram, H. Real-time computing without stable states: a new framework for neural computation based on perturbations. Neural Comput. 14, 2531–2560 (2002).
Google Scholar
Sun, C. et al. A systematic review of echo state networks from design to application. IEEE Trans. Artif. Intell. 5, 23–37 (2024).
Google Scholar
Tanaka, G. et al. Recent advances in physical reservoir computing: a review. Neural Netw. 115, 100–123 (2019).
Google Scholar
Lee, O. et al. Perspective on unconventional computing using magnetic skyrmions. Appl. Phys. Lett. 122, 260501 (2023).
Google Scholar
Liang, X. et al. Physical reservoir computing with emerging electronics. Nat. Electron. 7, 193–206 (2024).
Google Scholar
Allwood, D. A. et al. A perspective on physical reservoir computing with nanomagnetic devices. Appl. Phys. Lett. 122, 040501 (2023).
Google Scholar
Yan, M. et al. Emerging opportunities and challenges for the future of reservoir computing. Nat. Commun. 15, 2056 (2024).
Google Scholar
Cisneros, H., Mikolov, T. &Sivic, J. Benchmarking learning efficiency in deep reservoir computing. In Proc. The 1st Conference on Lifelong Learning Agents 532–547 (PMLR, 2022).
Manneschi, L., Lin, A. C. & Vasilaki, E. SpaRCe: Improved Learning of Reservoir Computing Systems Through Sparse Representations. IEEE Trans. Neural Netw. Learn. Syst. 34, 824–838 (2023).
Google Scholar
Manneschi, L. et al. Exploiting multiple timescales in hierarchical echo state networks. Front. Appl. Math. Stat. 6, 616658 (2021).
Google Scholar
Manneschi, L., Lin, A. C. & Vasilaki, E. Sparce: improved learning of reservoir computing systems through sparse representations. IEEE Trans. Neural Netw. Learn. Syst. 34, 824–838 (2021).
Google Scholar
Torrejon, J. et al. Neuromorphic computing with nanoscale spintronic oscillators. Nature 547, 428–431 (2017).
Google Scholar
Kanao, T. et al. Reservoir computing on spin-torque oscillator array. Phys. Rev. Appl. 12, 024052 (2019).
Google Scholar
Tsunegi, S. et al. Evaluation of memory capacity of spin torque oscillator for recurrent neural networks. Jpn. J. Appl. Phys. 57, 120307 (2018).
Google Scholar
Akashi, N. et al. Input-driven bifurcations and information processing capacity in spintronics reservoirs. Phys. Rev. Res. 2, 043303 (2020).
Google Scholar
Wu, X., Tong, Z. & Shao, Q. Optimizing reservoir computing based on an alternating input-driven spin-torque oscillator. Phys. Rev. Appl. 20, 024069 (2023).
Google Scholar
Tsunegi, S. et al. Information processing capacity of spintronic oscillator. Adv. Intell. Syst. 5, 2300175 (2023).
Google Scholar
Ababei, R. V. et al. Neuromorphic computation with a single magnetic domain wall. Sci. Rep. 11, 15587 (2021).
Google Scholar
Zhou, J. et al. Harnessing spatiotemporal transformation in magnetic domains for nonvolatile physical reservoir computing. Sci. Adv. 11, eadr5262 (2025).
Google Scholar
Watt, S., Kostylev, M., Ustinov, A. B. & Kalinikos, B. A. Implementing a magnonic reservoir computer model based on time-delay multiplexing. Phys. Rev. Appl. 15, 064060 (2021).
Google Scholar
Nakane, R., Hirose, A. & Tanaka, G. Spin waves propagating through a stripe magnetic domain structure and their applications to reservoir computing. Phys. Rev. Res. 3, 033243 (2021).
Google Scholar
Namiki, W. et al. Experimental demonstration of high-performance physical reservoir computing with nonlinear interfered spin wave multidetection. Adv. Intell. Syst. 5, 2300228 (2023).
Google Scholar
Namiki, W., Nishioka, D., Tsuchiya, T. & Terabe, K. Fast physical reservoir computing, achieved with nonlinear interfered spin waves. Neuromorphic Comput. Eng. 4, 024015 (2024).
Google Scholar
Iihama, S., Koike, Y., Mizukami, S. & Yoshinaga, N. Universal scaling between wave speed and size enables nanoscale high-performance reservoir computing based on propagating spin-waves. npj Spintron. 2, 5 (2024).
Google Scholar
Nagase, S., Nezu, S. & Sekiguchi, K. Spin-wave reservoir chips with short-term memory for high-speed estimation of external magnetic fields. Phys. Rev. Appl. 22, 024072 (2024).
Google Scholar
Gartside, J. C. et al. Reconfigurable training and reservoir computing in an artificial spin-vortex ice via spin-wave fingerprinting. Nat. Nanotechnol. 17, 460–469 (2022).
Google Scholar
Stenning, K. D. et al. Neuromorphic overparameterisation and few-shot learning in multilayer physical neural networks. Nat. Commun. 15, 7377 (2024).
Google Scholar
Hu, W. et al. Distinguishing artificial spin ice states using magnetoresistance effect for neuromorphic computing. Nat. Commun. 14, 2562 (2023).
Google Scholar
Hon, K. et al. Numerical simulation of artificial spin ice for reservoir computing. Appl. Phys. Express 14, 033001 (2021).
Google Scholar
Jensen, J. H., Folven, E. & Tufte, G. Computation in artificial spin ice. In Proc. IEEE Symposium on Artificial Life 15–22 (MIT Press, 2018).
Vidamour, I. et al. Reconfigurable reservoir computing in a magnetic metamaterial. Commun. Phys. 6, 230 (2023).
Google Scholar
Dawidek, R. W. et al. Dynamically driven emergence in a nanomagnetic system. Adv. Funct. Mater. 31, 2008389 (2021).
Google Scholar
Körber, L. et al. Pattern recognition in reciprocal space with a magnon-scattering reservoir. Nat. Commun. 14, 3954 (2023).
Google Scholar
Prychynenko, D. et al. Magnetic skyrmion as a nonlinear resistive element: a potential building block for reservoir computing. Phys. Rev. Appl. 9, 014034 (2018).
Google Scholar
Pinna, D., Bourianoff, G. & Everschor-Sitte, K. Reservoir computing with random skyrmion textures. Phys. Rev. Appl. 14, 054020 (2020).
Google Scholar
Raab, K. et al. Brownian reservoir computing realized using geometrically confined skyrmion dynamics. Nat. Commun. 13, 6982 (2022).
Google Scholar
Yokouchi, T. et al. Pattern recognition with neuromorphic computing using magnetic field-induced dynamics of skyrmions. Sci. Adv. 8, eabq5652 (2022).
Google Scholar
Lee, O. et al. Task-adaptive physical reservoir computing. Nat. Mater. 23, 79–87 (2024).
Google Scholar
Lee, M.-K. & Mochizuki, M. Handwritten digit recognition by spin waves in a skyrmion reservoir. Sci. Rep. 13, 19423 (2023).
Google Scholar
Msiska, R., Love, J., Mulkers, J., Leliaert, J. & Everschor-Sitte, K. Audio classification with skyrmion reservoirs. Adv. Intell. Syst. 5, 2200388 (2023).
Google Scholar
Everschor-Sitte, K., Majumdar, A., Wolk, K. & Meier, D. Topological magnetic and ferroelectric systems for reservoir computing. Nat. Rev. Phys. 6, 455–462 (2024).
Google Scholar
Cucchi, M., Abreu, S., Ciccone, G., Brunner, D. & Kleemann, H. Hands-on reservoir computing: a tutorial for practical implementation. Neuromorphic Comput. Eng. 2, 032002 (2022).
Google Scholar
Youel, H. et al. PRCpy: a Python package for processing of physical reservoir computing. Preprint at https://arxiv.org/abs/2410.18356 (2024).
Gurevich, A. G. & Melkov, G. A. Magnetization Oscillations and Waves (CRC Press, 2020).
Ralph, D. & Stiles, M. Spin transfer torques. J. Magn. Magn. Mater. 320, 1190–1216 (2008).
Google Scholar
Manchon, A. et al. Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems. Rev. Mod. Phys. 91, 035004 (2019).
Google Scholar
Jaeger, H. Tutorial on Training Recurrent Neural Networks, Covering BPPT, RTRL, EKF and the Echo State Network Approach Vol. 5 (GMD-Forschungszentrum Informationstechnik, 2002).
Love, J. et al. Spatial analysis of physical reservoir computers. Phys. Rev. Appl. 20, 044057 (2023).
Google Scholar
Dambre, J., Verstraeten, D., Schrauwen, B. & Massar, S. Information processing capacity of dynamical systems. Sci. Rep. 2, 514 (2012).
Google Scholar
Du, C. et al. Reservoir computing using dynamic memristors for temporal information processing. Nat. Commun. 8, 2204 (2017).
Google Scholar
Moon, J. et al. Temporal data classification and forecasting using a memristor-based reservoir computing system. Nat. Electron. 2, 480–487 (2019).
Google Scholar
Zhong, Y. et al. Dynamic memristor-based reservoir computing for high-efficiency temporal signal processing. Nat. Commun. 12, 408 (2021).
Google Scholar
Duport, F., Schneider, B., Smerieri, A., Haelterman, M. & Massar, S. All-optical reservoir computing. Opt. Express 20, 22783–22795 (2012).
Google Scholar
Pauwels, J., Verschaffelt, G., Massar, S. & Van der Sande, G. Distributed Kerr non-linearity in a coherent all-optical fiber-ring reservoir computer. Front. Phys. 7, 138 (2019).
Google Scholar
Hülser, T., Köster, F., Lüdge, K. & Jaurigue, L. Deriving task specific performance from the information processing capacity of a reservoir computer. Nanophotonics 12, 937–947 (2023).
Google Scholar
Roy, O. & Vetterli, M. The effective rank: a measure of effective dimensionality. In Proc. 15th European Signal Processing Conference (EUSIPCO 2007) 606–610 (IEEE, 2007).
Gallicchio, C. & Micheli, A. A Markovian characterization of redundancy in echo state networks by PCA. In Proc. 18th European Symposium on Artificial Neural Networks (ESANN, 2010).
Bianchi, F. M., Scardapane, S., Løkse, S. & Jenssen, R. Reservoir computing approaches for representation and classification of multivariate time series. IEEE Trans. Neural Netw. Learn. Syst. 32, 2169–2179 (2020).
Google Scholar
Wang, Y., Cao, J., Kurths, J. & Yanchuk, S. Universal bifurcation scenarios in delay-differential equations with one delay. J. Differ. Equ. 406, 366–396 (2024).
Google Scholar
Nakajima, K., Hauser, H., Li, T. & Pfeifer, R. Information processing via physical soft body. Sci. Rep. 5, 10487 (2015).
Google Scholar
Duport, F., Smerieri, A., Akrout, A., Haelterman, M. & Massar, S. Fully analogue photonic reservoir computer. Sci. Rep. 6, 22381 (2016).
Google Scholar
Kan, S. et al. Simple reservoir computing capitalizing on the nonlinear response of materials: theory and physical implementations. Phys. Rev. Appl. 15, 024030 (2021).
Google Scholar
Appeltant, L., Van der Sande, G., Danckaert, J. & Fischer, I. Constructing optimized binary masks for reservoir computing with delay systems. Sci. Rep. 4, 3629 (2014).
Google Scholar
Sugano, C., Kanno, K. & Uchida, A. Reservoir computing using multiple lasers with feedback on a photonic integrated circuit. IEEE J. Sel. Top. Quantum Electron. 26, 1–9 (2020).
Google Scholar
Sun, Y. et al. Experimental demonstration of a skyrmion-enhanced strain-mediated physical reservoir computing system. Nat. Commun. 14, 3434 (2023).
Google Scholar
Li, H. et al. Physical reservoir computing and deep neural networks using artificial and natural noncollinear spin textures. Phys. Rev. Appl. 22, 014027 (2024).
Google Scholar
Paquot, Y. et al. Optoelectronic reservoir computing. Sci. Rep. 2, 287 (2012).
Google Scholar
Watt, S. & Kostylev, M. Spoken digit classification using a spin-wave delay-line active-ring reservoir computing. Preprint at https://arxiv.org/abs/2005.12557 (2020).
Dodge, Y. in The Concise Encyclopedia of Statistics 502–505 (Springer, 2008).
Xie, K., Cao, J., Wang, X. & Wen, J. Optimal resource allocation for reliable and energy efficient cooperative communications. IEEE Trans. Wirel. Commun. 12, 4994–5007 (2013).
Google Scholar
Yang, J. & Ulukus, S. Optimal packet scheduling in an energy harvesting communication system. IEEE Trans. Commun. 60, 220–230 (2011).
Google Scholar
Barahona, F., Grötschel, M., Jünger, M. & Reinelt, G. An application of combinatorial optimization to statistical physics and circuit layout design. Oper. Res. 36, 493–513 (1988).
Google Scholar
Ushijima-Mwesigwa, H., Negre, C. F. & Mniszewski, S. M. Graph partitioning using quantum annealing on the d-wave system. In Proc. 2nd International Workshop on Post Moores Era Supercomputing 22–29 (Association for Computing Machinery, 2017).
Blunt, N. S. et al. Perspective on the current state-of-the-art of quantum computing for drug discovery applications. J. Chem. Theory Comput. 18, 7001–7023 (2022).
Google Scholar
Wu, Z. et al. Moleculenet: a benchmark for molecular machine learning. Chem. Sci. 9, 513–530 (2018).
Google Scholar
Laporte, G. The vehicle routing problem: an overview of exact and approximate algorithms. Eur. J. Oper. Res. 59, 345–358 (1992).
Google Scholar
Neukart, F. et al. Traffic flow optimization using a quantum annealer. Front. ICT 4, 29 (2017).
Google Scholar
Fernandez, S. A., Juan, A. A., de Armas Adrian, J., e Silva, D. G. & Terrén, D. R. Metaheuristics in telecommunication systems: network design, routing, and allocation problems. IEEE Syst. J. 12, 3948–3957 (2018).
Google Scholar
Böhm, F., Alonso-Urquijo, D., Verschaffelt, G. & Van der Sande, G. Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning. Nat. Commun. 13, 5847 (2022).
Google Scholar
Laydevant, J., Marković, D. & Grollier, J. Training an Ising machine with equilibrium propagation. Nat. Commun. 15, 3671 (2024).
Google Scholar
Johnson, M. W. et al. Quantum annealing with manufactured spins. Nature 473, 194–198 (2011).
Google Scholar
Honjo, T. et al. 100,000-spin coherent Ising machine. Sci. Adv. 7, eabh0952 (2021).
Google Scholar
Böhm, F., Verschaffelt, G. & Van der Sande, G. A poor man’s coherent Ising machine based on opto-electronic feedback systems for solving optimization problems. Nat. Commun. 10, 3538 (2019).
Google Scholar
Wang, T. & Roychowdhury, J. in Unconventional Computation and Natural Computation (eds McQuillan, I. & Seki, S.) 232–256 (Springer, 2019).
Cen, Q. et al. Large-scale coherent Ising machine based on optoelectronic parametric oscillator. Light. Sci. Appl. 11, 333 (2022).
Google Scholar
Lucas, A. Ising formulations of many NP problems. Front. Phys. 2, 5 (2014).
Google Scholar
Albertsson, D. I. et al. Ultrafast Ising machines using spin torque nano-oscillators. Appl. Phys. Lett. 118 (2021).
Houshang, A. et al. Phase-binarized spin Hall nano-oscillator arrays: towards spin Hall Ising machines. Phys. Rev. Appl. 17, 014003 (2022).
Google Scholar
González, V. H., Litvinenko, A., Kumar, A., Khymyn, R. & Åkerman, J. Spintronic devices as next-generation computation accelerators. Curr. Opin. Solid State Mater. Sci. 31, 101173 (2024).
Google Scholar
Litvinenko, A. et al. A spinwave Ising machine. Commun. Phys. 6, 227 (2023).
Google Scholar
McGoldrick, B. C., Sun, J. Z. & Liu, L. Ising machine based on electrically coupled spin Hall nano-oscillators. Phys. Rev. Appl. 17, 014006 (2022).
Google Scholar
Liu, Y.-T., Peng, C.-C., Hung, T.-Y., Huang, Y.-H. & Pai, C.-F. Advancing the problem-solving capabilities of Ising machines based on spin Hall nano-oscillators. Phys. Rev. Appl. 22, 064009 (2024).
Google Scholar
Behera, N. et al. Ultra-large mutually synchronized networks of 10 nm spin Hall nano-oscillators. Preprint at https://arxiv.org/abs/2501.18321 (2025).
Zahedinejad, M. et al. Memristive control of mutual spin hall nano-oscillator synchronization for neuromorphic computing. Nat. Mater. 21, 81–87 (2022).
Google Scholar
Kumar, A. et al. Spin-wave-mediated mutual synchronization and phase tuning in spin Hall nano-oscillators. Nat. Phys. 21, 245–252 (2025).
Google Scholar
Zahedinejad, M. et al. Two-dimensional mutually synchronized spin Hall nano-oscillator arrays for neuromorphic computing. Nat. Nanotechnol. 15, 47–52 (2020).
Google Scholar
Divinskiy, B. et al. Dispersionless propagation of ultrashort spin-wave pulses in ultrathin yttrium iron garnet waveguides. Phys. Rev. Appl. 16, 024028 (2021).
Google Scholar
Tatsumura, K., Hidaka, R., Nakayama, J., Kashimata, T. & Yamasaki, M. Real-time trading system based on selections of potentially profitable, uncorrelated, and balanced stocks by np-hard combinatorial optimization. IEEE Access 11, 120023–120033 (2023).
Google Scholar
Bybee, C. et al. Efficient optimization with higher-order Ising machines. Nat. Commun. 14, 6033 (2023).
Google Scholar
Inoue, K., Yoshida, K. & Kitahara, S. Coherent Potts machine based on an optical loop with a multilevel phase-sensitive amplifier. Opt. Commun. 528, 129022 (2023).
Google Scholar
Inaba, K. et al. Potts model solver based on hybrid physical and digital architecture. Commun. Phys. 5, 137 (2022).
Google Scholar
Bashar, M. K., Li, Z., Narayanan, V. & Shukla, N. An FPGA-based Max-K-Cut accelerator exploiting oscillator synchronization model. In Proc. 25th International Symposium on Quality Electronic Design (ISQED) 1–8 (IEEE, 2024).
Calvanese Strinati, M. & Conti, C. Hyperscaling in the coherent hyperspin machine. Phys. Rev. Lett. 132, 017301 (2024).
Google Scholar
Litvinenko, A., Khymyn, R., Ovcharov, R. & Åkerman, J. A 50-spin surface acoustic wave Ising machine. Commun. Phys. 8, 58 (2025).
Google Scholar
Tchendjou, G. T., Danouchi, K., Prenat, G. & Anghel, L. Spintronic memristor-based binarized ensemble convolutional neural network architectures. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 42, 1885–1897 (2022).
Google Scholar
Li, C. et al. Analogue signal and image processing with large memristor crossbars. Nat. Electron. 1, 52–59 (2018).
Google Scholar
Hung, J.-H. A Study on Advanced Ising Machine Designs: BLIM, King’s Graph Mapping, and OIM Chips. MSc thesis, Univ. California, Berkeley (2024).
Okuyama, T., Yoshimura, C., Hayashi, M., Tanaka, S. & Yamaoka, M. Contractive graph-minor embedding for cmos ising computer. IEICE Tech. Rep. 116, 97–103 (2016).
Sugie, Y. et al. Minor-embedding heuristics for large-scale annealing processors with sparse hardware graphs of up to 102,400 nodes. Soft Comput. 25, 1731–1749 (2021).
Google Scholar
Kumar, A. et al. Robust mutual synchronization in long spin Hall nano-oscillator chains. Nano Lett. 23, 6720–6726 (2023).
Google Scholar
Dutta, S. et al. Experimental demonstration of phase transition nano-oscillator based Ising machine. In Proc. 2019 IEEE International Electron Devices Meeting (IEDM) 37.8.1–37.8.4 (IEEE, 2019).
Dutta, S. et al. An Ising Hamiltonian solver based on coupled stochastic phase-transition nano-oscillators. Nat. Electron. 4, 502–512 (2021).
Google Scholar
King, A. D., Bernoudy, W., King, J., Berkley, A. J. & Lanting, T. Emulating the coherent Ising machine with a mean-field algorithm. Preprint at https://arxiv.org/abs/1806.08422 (2018).
Sharma, R. et al. Nanoscale spin rectifiers for harvesting ambient radiofrequency energy. Nat. Electron. 7, 653–661 (2024).
Google Scholar
Chen, A. et al. Giant nonvolatile manipulation of magnetoresistance in magnetic tunnel junctions by electric fields via magnetoelectric coupling. Nat. Commun. 10, 243 (2019).
Google Scholar
Sun, W. et al. Electric field control of perpendicular magnetic tunnel junctions with easy-cone magnetic anisotropic free layers. Sci. Adv. 10, eadj8379 (2024).
Google Scholar
Wu, W., Yaw Ameyaw, C., Doty, M. F. & Jungfleisch, M. B. Principles of spintronic THz emitters. J. Appl. Phys. 130, 091101 (2021).
Google Scholar
Aadit, N. A. et al. Massively parallel probabilistic computing with sparse Ising machines. Nat. Electron. 5, 460–468 (2022).
Google Scholar
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, 1–11 (2024).
Google Scholar
Niazi, M. A. & Camsari, K. Y. CMOS plus stochastic nanomagnets enabling heterogeneous probabilistic computing platforms. Nat. Commun. 15, 1–9 (2024).
Google Scholar
Yang, S. et al. 250 magnetic tunnel junctions-based probabilistic Ising machine. Preprint at https://arxiv.org/abs/2506.14590 (2025).
Erokhin, S. & Berkov, D. Robust synchronization of an arbitrary number of spin-torque-driven vortex nano-oscillators. Phys. Rev. B 89, 144421 (2014).
Google Scholar
Chen, H.-H. et al. Phase locking of spin-torque nano-oscillator pairs with magnetic dipolar coupling. Phys. Rev. B 93, 224410 (2016).
Google Scholar
Kendziorczyk, T., Demokritov, S. & Kuhn, T. Spin-wave-mediated mutual synchronization of spin-torque nano-oscillators: A micromagnetic study of multistable phase locking. Phys. Rev. B 90, 054414 (2014).
Google Scholar
Houshang, A. et al. Spin-wave-beam driven synchronization of nanocontact spin-torque oscillators. Nat. Nanotechnol. 11, 280–286 (2016).
Google Scholar
Kendziorczyk, T. & Kuhn, T. Mutual synchronization of nanoconstriction-based spin hall nano-oscillators through evanescent and propagating spin waves. Phys. Rev. B 93, 134413 (2016).
Google Scholar
Locatelli, N. et al. Efficient synchronization of dipolarly coupled vortex-based spin transfer nano-oscillators. Sci. Rep. 5, 17039 (2015).
Google Scholar
Sharma, R. et al. Electrically connected spin-torque oscillators array for 2.4 GHz WiFi band transmission and energy harvesting. Nat. Commun. 12, 2924 (2021).
Google Scholar
Fetisov, Y., Kabos, P. & Patton, C. Active magnetostatic wave delay line. IEEE Trans. Magn. 34, 259–271 (1998).
Google Scholar
Sethares, J., Owens, J. & Smith, C. Msw nondispersive, electronically tunable time delay elements. Electron. Lett. 16, 825–826 (1980).
Google Scholar
Merbouche, H. et al. True amplification of spin waves in magnonic nano-waveguides. Nat. Commun. 15, 1560 (2024).
Google Scholar
Vidamour, I. T. et al. Quantifying the computational capability of a nanomagnetic reservoir computing platform with emergent magnetisation dynamics. Nanotechnology 33, 485203 (2022).
Google Scholar
Taniguchi, T., Ogihara, A., Utsumi, Y. & Tsunegi, S. Spintronic reservoir computing without driving current or magnetic field. Sci. Rep. 12, 10627 (2022).
Google Scholar
Watt, S., Kostylev, M. & Ustinov, A. B. Enhancing computational performance of a spin-wave reservoir computer with input synchronization. J. Appl. Phys. 129, 044902 (2021).
Google Scholar
Watt, S. & Kostylev, M. Reservoir computing using a spin-wave delay-line active-ring resonator based on yttrium-iron-garnet film. Phys. Rev. Appl. 13, 034057 (2020).
Google Scholar
Nakane, R., Tanaka, G. & Hirose, A. Reservoir computing with spin waves excited in a garnet film. IEEE Access 6, 4462–4469 (2018).
Google Scholar
Soumah, L. et al. Entropy-assisted nanosecond stochastic operation in perpendicular superparamagnetic tunnel junctions. Phys. Rev. Appl. 24, L011002 (2024).
Google Scholar
