1
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Laydevant J, Marković D, Grollier J. Training an Ising machine with equilibrium propagation. Nat Commun 2024; 15:3671. [PMID: 38693108 PMCID: PMC11063034 DOI: 10.1038/s41467-024-46879-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 03/12/2024] [Indexed: 05/03/2024] Open
Abstract
Ising machines, which are hardware implementations of the Ising model of coupled spins, have been influential in the development of unsupervised learning algorithms at the origins of Artificial Intelligence (AI). However, their application to AI has been limited due to the complexities in matching supervised training methods with Ising machine physics, even though these methods are essential for achieving high accuracy. In this study, we demonstrate an efficient approach to train Ising machines in a supervised way through the Equilibrium Propagation algorithm, achieving comparable results to software-based implementations. We employ the quantum annealing procedure of the D-Wave Ising machine to train a fully-connected neural network on the MNIST dataset. Furthermore, we demonstrate that the machine's connectivity supports convolution operations, enabling the training of a compact convolutional network with minimal spins per neuron. Our findings establish Ising machines as a promising trainable hardware platform for AI, with the potential to enhance machine learning applications.
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Affiliation(s)
- Jérémie Laydevant
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767, Palaiseau, France.
| | - Danijela Marković
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767, Palaiseau, France
| | - Julie Grollier
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767, Palaiseau, France.
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2
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Liao Z, Shi Z, Sarker MS, Tabata H. Robust QRS detection based on simulated degenerate optical parametric oscillator-assisted neural network. Heliyon 2024; 10:e28903. [PMID: 38576550 PMCID: PMC10990971 DOI: 10.1016/j.heliyon.2024.e28903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Revised: 03/22/2024] [Accepted: 03/26/2024] [Indexed: 04/06/2024] Open
Abstract
Accurately detecting the depolarization QRS complex in the ventricles is a fundamental requirement for cardiovascular disease detection using electrocardiography (ECG). In contrast to traditional signal enhancement algorithms, emerging neural network approaches have shown promise for QRS detection because of their generalizability on complex data. However, the inevitable noise present during ECG recording leads to a decrease in the performance of neural networks. To enhance the robustness and performance of neural network-based QRS detectors, we propose a simulated degeneration unit (SDU)-assisted convolutional neural network (CNN). An SDU simulates the physical degeneration process of interfering optical pulses, which can effectively suppress in-band noise. Through comprehensive performance evaluations on three open-source databases, the SDU-enhanced CNN-based approach demonstrated better performance in detecting QRS complexes than other recently reported QRS detectors. Furthermore, real-world noise injection tests indicate that the optimal noise robustness boundary for the CNN equipped with SDU is 167-300% higher than that for the CNN without SDU.
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Affiliation(s)
- Zhiqiang Liao
- Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
- Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
| | - Zhuozheng Shi
- Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
- Bioinformatics Interdepartmental Program, University of California Los Angeles, Los Angeles, CA, USA
| | - Md Shamim Sarker
- Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
- Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
| | - Hitoshi Tabata
- Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
- Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
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3
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Casilli N, Kaisar T, Colombo L, Ghosh S, Feng PXL, Cassella C. Parametric Frequency Divider Based Ising Machines. PHYSICAL REVIEW LETTERS 2024; 132:147301. [PMID: 38640363 DOI: 10.1103/physrevlett.132.147301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2023] [Accepted: 02/20/2024] [Indexed: 04/21/2024]
Abstract
We report on a new class of Ising machines (IMs) that rely on coupled parametric frequency dividers (PFDs) as macroscopic artificial spins. Unlike the IM counterparts based on subharmonic-injection locking (SHIL), PFD IMs do not require strong injected continuous-wave signals or applied dc voltages. Therefore, they show a significantly lower power consumption per spin compared to SHIL-based IMs, making it feasible to accurately solve large-scale combinatorial optimization problems that are hard or even impossible to solve by using the current von Neumann computing architectures. Furthermore, using high quality factor resonators in the PFD design makes PFD IMs able to exhibit a nanowatt-level power per spin. Also, it remarkably allows a speedup of the phase synchronization among the PFDs, resulting in shorter time to solution and lower energy to solution despite the resonators' longer relaxation time. As a proof of concept, a 4-node PFD IM has been demonstrated. This IM correctly solves a set of Max-Cut problems while consuming just 600 nanowatts per spin. This power consumption is 2 orders of magnitude lower than the power per spin of state-of-the-art SHIL-based IMs operating at the same frequency.
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Affiliation(s)
- Nicolas Casilli
- Department of Electrical and Computer Engineering, Northeastern University, Boston, Massachusetts 02115, USA
| | - Tahmid Kaisar
- Department of Electrical and Computer Engineering, University of Florida, Gainesville, Florida 32611, USA
| | - Luca Colombo
- Department of Electrical and Computer Engineering, Northeastern University, Boston, Massachusetts 02115, USA
| | - Siddhartha Ghosh
- Department of Electrical and Computer Engineering, Northeastern University, Boston, Massachusetts 02115, USA
| | - Philip X-L Feng
- Department of Electrical and Computer Engineering, University of Florida, Gainesville, Florida 32611, USA
| | - Cristian Cassella
- Department of Electrical and Computer Engineering, Northeastern University, Boston, Massachusetts 02115, USA
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4
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Yin X, Qian Y, Vardar A, Günther M, Müller F, Laleni N, Zhao Z, Jiang Z, Shi Z, Shi Y, Gong X, Zhuo C, Kämpfe T, Ni K. Ferroelectric compute-in-memory annealer for combinatorial optimization problems. Nat Commun 2024; 15:2419. [PMID: 38499524 PMCID: PMC10948773 DOI: 10.1038/s41467-024-46640-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2023] [Accepted: 03/05/2024] [Indexed: 03/20/2024] Open
Abstract
Computationally hard combinatorial optimization problems (COPs) are ubiquitous in many applications. Various digital annealers, dynamical Ising machines, and quantum/photonic systems have been developed for solving COPs, but they still suffer from the memory access issue, scalability, restricted applicability to certain types of COPs, and VLSI-incompatibility, respectively. Here we report a ferroelectric field effect transistor (FeFET) based compute-in-memory (CiM) annealer for solving larger-scale COPs efficiently. Our CiM annealer converts COPs into quadratic unconstrained binary optimization (QUBO) formulations, and uniquely accelerates in-situ the core vector-matrix-vector (VMV) multiplication operations of QUBO formulations in a single step. Specifically, the three-terminal FeFET structure allows for lossless compression of the stored QUBO matrix, achieving a remarkably 75% chip size saving when solving Max-Cut problems. A multi-epoch simulated annealing (MESA) algorithm is proposed for efficient annealing, achieving up to 27% better solution and ~ 2X speedup than conventional simulated annealing. Experimental validation is performed using the first integrated FeFET chip on 28nm HKMG CMOS technology, indicating great promise of FeFET CiM array in solving general COPs.
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Affiliation(s)
- Xunzhao Yin
- Zhejiang University, Hangzhou, China
- Key Laboratory of CS&AUS of Zhejiang Province, Hangzhou, China
| | - Yu Qian
- Zhejiang University, Hangzhou, China
| | | | | | | | | | | | | | - Zhiguo Shi
- Zhejiang University, Hangzhou, China
- Key Laboratory of CS&AUS of Zhejiang Province, Hangzhou, China
| | - Yiyu Shi
- University of Notre Dame, Notre Dame, USA
| | - Xiao Gong
- National University of Singapore, Singapore, Singapore
| | - Cheng Zhuo
- Zhejiang University, Hangzhou, China.
- Key Laboratory of CS&AUS of Zhejiang Province, Hangzhou, China.
| | | | - Kai Ni
- University of Notre Dame, Notre Dame, USA.
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5
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Jiang Z, Chen G, Qiao R, Feng P, Chen Y, Su J, Zhao Z, Jin M, Chen X, Li Z, Lu H. Point convolutional neural network algorithm for Ising model ground state research based on spring vibration. Sci Rep 2024; 14:2643. [PMID: 38302489 PMCID: PMC11224306 DOI: 10.1038/s41598-023-49559-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2023] [Accepted: 12/09/2023] [Indexed: 02/03/2024] Open
Abstract
The ground state search of the Ising model can be used to solve many combinatorial optimization problems. Under the current computer architecture, an Ising ground state search algorithm suitable for hardware computing is necessary for solving practical problems. Inspired by the potential energy conversion of the springs, we propose the Spring-Ising Algorithm, a point convolutional neural network algorithm for ground state search based on the spring vibration model. Spring-Ising Algorithm regards the spin as a moving mass point connected to a spring and establishes the equation of motion for all spins. Spring-Ising Algorithm can be mapped on AI chips through the basic structure of the neural network for fast and efficient parallel computing. The algorithm has shown promising results in solving the Ising model and has been tested in the recognized test benchmark K2000. The optimal results of this algorithm after 10,000 steps of iteration are 2.9% of all results. The algorithm introduces the concept of dynamic equilibrium to achieve a more detailed local search by dynamically adjusting the weight of the Ising model in the spring oscillation model. Spring-Ising Algorithm offers the possibility to calculate the Ising model on a chip which focuses on accelerating neural network calculations.
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Affiliation(s)
- Zhelong Jiang
- Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- Materials and Optoelectronics Research Center, University of Chinese Academy of Sciences, Beijing, China
| | - Gang Chen
- Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China.
| | - Ruixiu Qiao
- Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
| | - Pengcheng Feng
- Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- Materials and Optoelectronics Research Center, University of Chinese Academy of Sciences, Beijing, China
| | - Yihao Chen
- Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- Materials and Optoelectronics Research Center, University of Chinese Academy of Sciences, Beijing, China
| | - Junjia Su
- Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- Materials and Optoelectronics Research Center, University of Chinese Academy of Sciences, Beijing, China
| | - Zhiyuan Zhao
- Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- School of Microelectronics, University of Science and Technology of China, Hefei, China
| | - Min Jin
- Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
| | - Xu Chen
- Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
| | - Zhigang Li
- Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
| | - Huaxiang Lu
- Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- Materials and Optoelectronics Research Center, University of Chinese Academy of Sciences, Beijing, China
- College of Microelectronics, University of Chinese Academy of Sciences, Beijing, China
- Semiconductor Neural Network Intelligent Perception and Computing Technology Beijing Key Laboratory, Beijing, China
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6
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Calvanese Strinati M, Conti C. Hyperscaling in the Coherent Hyperspin Machine. PHYSICAL REVIEW LETTERS 2024; 132:017301. [PMID: 38242655 DOI: 10.1103/physrevlett.132.017301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Revised: 11/06/2023] [Accepted: 12/06/2023] [Indexed: 01/21/2024]
Abstract
Classical and quantum systems are used to simulate the Ising Hamiltonian, an essential component in large-scale optimization and machine learning. However, as the system size increases, devices like quantum annealers and coherent Ising machines face an exponential drop in their success rate. Here, we introduce a novel approach involving high-dimensional embeddings of the Ising Hamiltonian and a technique called "dimensional annealing" to counteract the decrease in performance. This approach leads to an exponential improvement in the success rate and other performance metrics, slowing down the decline in performance as the system size grows. A thorough examination of convergence dynamics in high-performance computing validates the new methodology. Additionally, we suggest practical implementations using technologies like coherent Ising machines, all-optical systems, and hybrid digital systems. The proposed hyperscaling heuristics can also be applied to other quantum or classical Ising devices by adjusting parameters such as nonlinear gain, loss, and nonlocal couplings.
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Affiliation(s)
| | - Claudio Conti
- Centro Ricerche Enrico Fermi (CREF), Via Panisperna 89a, 00184 Rome, Italy
- Physics Department, Sapienza University of Rome, 00185 Rome, Italy
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7
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Luo L, Mi Z, Huang J, Ruan Z. Wavelength-division multiplexing optical Ising simulator enabling fully programmable spin couplings and external magnetic fields. SCIENCE ADVANCES 2023; 9:eadg6238. [PMID: 38039362 PMCID: PMC10691765 DOI: 10.1126/sciadv.adg6238] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Accepted: 11/02/2023] [Indexed: 12/03/2023]
Abstract
Recently various physical systems have been proposed for modeling Ising spin Hamiltonians appealing to solve combinatorial optimization problems with remarkable performance. However, how to implement arbitrary spin-spin interactions is a critical and challenging problem in unconventional Ising machines. Here, we propose a general gauge transformation scheme to enable arbitrary spin-spin interactions and external magnetic fields as well, by decomposing an Ising Hamiltonian into multiple Mattis-type interactions. With this scheme, a wavelength-division multiplexing spatial photonic Ising machine (SPIM) is developed to show the programmable capability of general spin coupling interactions. We exploit the wavelength-division multiplexing SPIM to simulate three spin systems: ±J models, Sherrington-Kirkpatrick models, and only locally connected J1-J2 models and observe the phase transitions. We also demonstrate the ground-state search for solving Max-Cut problem with the wavelength-division multiplexing SPIM. These results promise the realization of ultrafast-speed and high-power efficiency Boltzmann sampling to a generalized large-scale Ising model.
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Affiliation(s)
- Li Luo
- School of Physics, State Key Laboratory of Extreme Photonics and Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Zhiyi Mi
- School of Physics, State Key Laboratory of Extreme Photonics and Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Junyi Huang
- School of Physics, State Key Laboratory of Extreme Photonics and Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Zhichao Ruan
- School of Physics, State Key Laboratory of Extreme Photonics and Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
- College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China
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8
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Sverdlov V, Choi SB. Editorial for the Special Issue on Magnetic and Spin Devices, Volume II. MICROMACHINES 2023; 14:2131. [PMID: 38004988 PMCID: PMC10672736 DOI: 10.3390/mi14112131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2023] [Accepted: 11/19/2023] [Indexed: 11/26/2023]
Abstract
Although the miniaturization of metal-oxide-semiconductor field effect transistors (MOSFETs)-the main driver behind an outstanding increase in the speed, performance, density, and complexity of modern integrated circuits-is continuing, numerous outstanding technological challenges in complimentary metal-oxide-semiconductor (CMOS) device miniaturization are slowly bringing the downscaling to saturation [...].
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Affiliation(s)
- Viktor Sverdlov
- Christian Doppler Laboratory for Nonvolatile Magnetoresistive Memory and Logic, Institute for Microelectronics, TU Wien, 1040 Vienna, Austria
| | - Seung-Bok Choi
- Department of Mechanical Engineering, The State University of New York at Korea (SUNY Korea), 119 Songdo Moonhwa-Ro, Yeonsu-Gu, Incheon 21985, Republic of Korea
- Department of Mechanical Engineering, Industrial University of Ho Chi Minh City, Ho Chi Minh City 7000, Vietnam
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9
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Bashar MK, Shukla N. Designing Ising machines with higher order spin interactions and their application in solving combinatorial optimization. Sci Rep 2023; 13:9558. [PMID: 37308674 DOI: 10.1038/s41598-023-36531-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 06/05/2023] [Indexed: 06/14/2023] Open
Abstract
The Ising model provides a natural mapping for many computationally hard combinatorial optimization problems (COPs). Consequently, dynamical system-inspired computing models and hardware platforms that minimize the Ising Hamiltonian, have recently been proposed as a potential candidate for solving COPs, with the promise of significant performance benefit. However, prior work on designing dynamical systems as Ising machines has primarily considered quadratic interactions among the nodes. Dynamical systems and models considering higher order interactions among the Ising spins remain largely unexplored, particularly for applications in computing. Therefore, in this work, we propose Ising spin-based dynamical systems that consider higher order (> 2) interactions among the Ising spins, which subsequently, enables us to develop computational models to directly solve many COPs that entail such higher order interactions (i.e., COPs on hypergraphs). Specifically, we demonstrate our approach by developing dynamical systems to compute the solution for the Boolean NAE-K-SAT (K ≥ 4) problem as well as solve the Max-K-Cut of a hypergraph. Our work advances the potential of the physics-inspired 'toolbox' for solving COPs.
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Affiliation(s)
- Mohammad Khairul Bashar
- Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA
| | - Nikhil Shukla
- Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA.
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10
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Wang J, Ebler D, Wong KYM, Hui DSW, Sun J. Bifurcation behaviors shape how continuous physical dynamics solves discrete Ising optimization. Nat Commun 2023; 14:2510. [PMID: 37130854 PMCID: PMC10154334 DOI: 10.1038/s41467-023-37695-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2022] [Accepted: 03/28/2023] [Indexed: 05/04/2023] Open
Abstract
Simulating physical dynamics to solve hard combinatorial optimization has proven effective for medium- to large-scale problems. The dynamics of such systems is continuous, with no guarantee of finding optimal solutions of the original discrete problem. We investigate the open question of when simulated physical solvers solve discrete optimizations correctly, with a focus on coherent Ising machines (CIMs). Having established the existence of an exact mapping between CIM dynamics and discrete Ising optimization, we report two fundamentally distinct bifurcation behaviors of the Ising dynamics at the first bifurcation point: either all nodal states simultaneously deviate from zero (synchronized bifurcation) or undergo a cascade of such deviations (retarded bifurcation). For synchronized bifurcation, we prove that when the nodal states are uniformly bounded away from the origin, they contain sufficient information for exactly solving the Ising problem. When the exact mapping conditions are violated, subsequent bifurcations become necessary and often cause slow convergence. Inspired by those findings, we devise a trapping-and-correction (TAC) technique to accelerate dynamics-based Ising solvers, including CIMs and simulated bifurcation. TAC takes advantage of early bifurcated "trapped nodes" which maintain their sign throughout the Ising dynamics to reduce computation time effectively. Using problem instances from open benchmark and random Ising models, we validate the superior convergence and accuracy of TAC.
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Affiliation(s)
- Juntao Wang
- Theory Lab, Central Research Institute, 2012 Labs, Huawei Technologies Co. Ltd., Hong Kong SAR, China
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong SAR, China
| | - Daniel Ebler
- Theory Lab, Central Research Institute, 2012 Labs, Huawei Technologies Co. Ltd., Hong Kong SAR, China.
| | - K Y Michael Wong
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong SAR, China
| | - David Shui Wing Hui
- Theory Lab, Central Research Institute, 2012 Labs, Huawei Technologies Co. Ltd., Hong Kong SAR, China
| | - Jie Sun
- Theory Lab, Central Research Institute, 2012 Labs, Huawei Technologies Co. Ltd., Hong Kong SAR, China.
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11
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Mwamsojo N, Lehmann F, Merghem K, Benkelfat BE, Frignac Y. Optoelectronic coherent Ising machine for combinatorial optimization problems. OPTICS LETTERS 2023; 48:2150-2153. [PMID: 37058664 DOI: 10.1364/ol.485215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Accepted: 03/20/2023] [Indexed: 06/19/2023]
Abstract
Hopfield networks are iterative procedures able to solve combinatorial optimization problems. New studies regarding algorithm-architecture adequacy are fostered by the re-emergence of hardware implementations of such methods in the form of Ising machines. In this work, we propose an optoelectronic architecture suitable for fast processing and low energy consumption. We show that our approach allows effective optimization relevant to statistical image denoising.
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12
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Rah Y, Jeong Y, Han S, Yu K. Low Power Coherent Ising Machine Based on Mechanical Kerr Nonlinearity. PHYSICAL REVIEW LETTERS 2023; 130:073802. [PMID: 36867813 DOI: 10.1103/physrevlett.130.073802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2022] [Accepted: 01/19/2023] [Indexed: 06/18/2023]
Abstract
Finding a reliable Ising machine for solving nondeterministic polynomial-class problems has attracted great attention in recent years, where an authentic system can be expanded with polynomial-scaled resources to find the ground state Ising Hamiltonian. In this Letter, we propose an extremely low power optomechanical coherent Ising machine based on a new enhanced symmetry breaking mechanism and highly nonlinear mechanical Kerr effect. The mechanical movement of an optomechanical actuator induced by the optical gradient force greatly increases the nonlinearity by a few orders and significantly reduces the power threshold using conventional structures capable of fabrication via photonic integrated circuit platforms. With the simple but strong bifurcation mechanism and remarkably low power requirement, our optomechanical spin model opens a path for chip-scale integration of large-size Ising machine implementations with great stability.
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Affiliation(s)
- Yoonhyuk Rah
- School of Electrical Engineering, Korea Advanced Institute of Science and Technology, KAIST, Daejeon 34141, Republic of Korea
| | - Youngjae Jeong
- School of Electrical Engineering, Korea Advanced Institute of Science and Technology, KAIST, Daejeon 34141, Republic of Korea
| | - Sangyoon Han
- Robotics and Mechatronics Engineering, Daegu-Gyeongbuk Institute of Science and Technology, DGIST, Daegu 42988, Republic of Korea
| | - Kyoungsik Yu
- School of Electrical Engineering, Korea Advanced Institute of Science and Technology, KAIST, Daejeon 34141, Republic of Korea
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13
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Prabhakar A, Shah P, Gautham U, Natarajan V, Ramesh V, Chandrachoodan N, Tayur S. Optimization with photonic wave-based annealers. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210409. [PMID: 36463927 DOI: 10.1098/rsta.2021.0409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2022] [Accepted: 08/14/2022] [Indexed: 06/17/2023]
Abstract
Many NP-hard combinatorial optimization (CO) problems can be cast as a quadratic unconstrained binary optimization model, which maps naturally to an Ising model. The final spin configuration in the Ising model can adiabatically arrive at a solution to a Hamiltonian, given a known set of interactions between spins. We enhance two photonic Ising machines (PIMs) and compare their performance against classical (Gurobi) and quantum (D-Wave) solvers. The temporal multiplexed coherent Ising machine (TMCIM) uses the bistable response of an electro-optic modulator to mimic the spin up and down states. We compare TMCIM performance on Max-cut problems. A spatial photonic Ising machine (SPIM) convolves the wavefront of a coherent laser beam with the pixel distribution of a spatial light modulator to adiabatically achieve a minimum energy configuration, and solve a number partitioning problem (NPP). Our computational results on Max-cut indicate that classical solvers are still a better choice, while our NPP results show that SPIM is better as the problem size increases. In both cases, connectivity in Ising hardware is crucial for performance. Our results also highlight the importance of better understanding which CO problems are most likely to benefit from which type of PIM. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- A Prabhakar
- Indian Institute of Technology Madras, Chennai 600036, India
| | - P Shah
- Indian Institute of Technology Madras, Chennai 600036, India
| | - U Gautham
- Indian Institute of Technology Madras, Chennai 600036, India
| | - V Natarajan
- Indian Institute of Technology Madras, Chennai 600036, India
| | - V Ramesh
- Indian Institute of Technology Madras, Chennai 600036, India
| | | | - S Tayur
- Carnegie Mellon University, Pittsburgh, PA 15213, USA
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14
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Chen W, Tang H, Wang Y, Hu X, Lin Y, Min T, Xie Y. E-Spin: A Stochastic Ising Spin Based on Electrically-Controlled MTJ for Constructing Large-Scale Ising Annealing Systems. MICROMACHINES 2023; 14:258. [PMID: 36837958 PMCID: PMC9962373 DOI: 10.3390/mi14020258] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/19/2022] [Revised: 01/01/2023] [Accepted: 01/14/2023] [Indexed: 06/18/2023]
Abstract
With its unique computer paradigm, the Ising annealing machine has become an emerging research direction. The Ising annealing system is highly effective at addressing combinatorial optimization (CO) problems that are difficult for conventional computers to tackle. However, Ising spins, which comprise the Ising system, are difficult to implement in high-performance physical circuits. We propose a novel type of Ising spin based on an electrically-controlled magnetic tunnel junction (MTJ). Electrical operation imparts true randomness, great stability, precise control, compact size, and easy integration to the MTJ-based spin. In addition, simulations demonstrate that the frequency of electrically-controlled stochastic Ising spin (E-spin) is 50 times that of the thermal disturbance MTJ-based spin (p-bit). To develop a large-scale Ising annealing system, up to 64 E-spins are implemented. Our Ising annealing system demonstrates factorization of integers up to 264 with a temporal complexity of around O(n). The proposed E-spin shows superiority in constructing large-scale Ising annealing systems and solving CO problems.
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Affiliation(s)
- Wenhan Chen
- State Key Laboratory of ASIC & System, School of Microelectronics, Fudan University, Shanghai 201203, China
| | - Haodi Tang
- State Key Laboratory of ASIC & System, School of Microelectronics, Fudan University, Shanghai 201203, China
| | - Yu Wang
- State Key Laboratory of ASIC & System, School of Microelectronics, Fudan University, Shanghai 201203, China
| | - Xianwu Hu
- State Key Laboratory of ASIC & System, School of Microelectronics, Fudan University, Shanghai 201203, China
| | - Yuming Lin
- State Key Laboratory of ASIC & System, School of Microelectronics, Fudan University, Shanghai 201203, China
| | - Tai Min
- Center for Spintronics and Quantum Systems, State Key Laboratory for Mechanical Behavior of Materials, Department of Materials Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China
| | - Yufeng Xie
- State Key Laboratory of ASIC & System, School of Microelectronics, Fudan University, Shanghai 201203, China
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15
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Calvanese Strinati M, Conti C. Multidimensional hyperspin machine. Nat Commun 2022; 13:7248. [PMID: 36433964 PMCID: PMC9700766 DOI: 10.1038/s41467-022-34847-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 11/08/2022] [Indexed: 11/26/2022] Open
Abstract
From condensed matter to quantum chromodynamics, multidimensional spins are a fundamental paradigm, with a pivotal role in combinatorial optimization and machine learning. Machines formed by coupled parametric oscillators can simulate spin models, but only for Ising or low-dimensional spins. Currently, machines implementing arbitrary dimensions remain a challenge. Here, we introduce and validate a hyperspin machine to simulate multidimensional continuous spin models. We realize high-dimensional spins by pumping groups of parametric oscillators, and show that the hyperspin machine finds to a very good approximation the ground state of complex graphs. The hyperspin machine can interpolate between different dimensions by tuning the coupling topology, a strategy that we call "dimensional annealing". When interpolating between the XY and the Ising model, the dimensional annealing substantially increases the success probability compared to conventional Ising simulators. Hyperspin machines are a new computational model for combinatorial optimization. They can be realized by off-the-shelf hardware for ultrafast, large-scale applications in classical and quantum computing, condensed-matter physics, and fundamental studies.
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Affiliation(s)
- Marcello Calvanese Strinati
- grid.449962.4Centro Ricerche Enrico Fermi (CREF), Via Panisperna 89a, 00184 Rome, Italy ,grid.472642.1Institute for Complex Systems, National Research Council (ISC-CNR), 00185 Rome, Italy
| | - Claudio Conti
- grid.449962.4Centro Ricerche Enrico Fermi (CREF), Via Panisperna 89a, 00184 Rome, Italy ,grid.472642.1Institute for Complex Systems, National Research Council (ISC-CNR), 00185 Rome, Italy ,grid.7841.aPhysics Department, Sapienza University of Rome, 00185 Rome, Italy
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16
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Cen Q, Ding H, Hao T, Guan S, Qin Z, Lyu J, Li W, Zhu N, Xu K, Dai Y, Li M. Large-scale coherent Ising machine based on optoelectronic parametric oscillator. LIGHT, SCIENCE & APPLICATIONS 2022; 11:333. [PMID: 36433949 PMCID: PMC9700853 DOI: 10.1038/s41377-022-01013-1] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/07/2022] [Revised: 10/08/2022] [Accepted: 10/11/2022] [Indexed: 06/16/2023]
Abstract
Ising machines based on analog systems have the potential to accelerate the solution of ubiquitous combinatorial optimization problems. Although some artificial spins to support large-scale Ising machines have been reported, e.g., superconducting qubits in quantum annealers and short optical pulses in coherent Ising machines, the spin stability is fragile due to the ultra-low equivalent temperature or optical phase sensitivity. In this paper, we propose to use short microwave pulses generated from an optoelectronic parametric oscillator as the spins to implement a large-scale Ising machine with high stability. The proposed machine supports 25,600 spins and can operate continuously and stably for hours. Moreover, the proposed Ising machine is highly compatible with high-speed electronic devices for programmability, paving a low-cost, accurate, and easy-to-implement way toward solving real-world optimization problems.
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Affiliation(s)
- Qizhuang Cen
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, China
| | - Hao Ding
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, China
| | - Tengfei Hao
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, China
| | - Shanhong Guan
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, China
| | - Zhiqiang Qin
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, China
| | - Jiaming Lyu
- School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai, China
| | - Wei Li
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, China
| | - Ninghua Zhu
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, China
| | - Kun Xu
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, China
| | - Yitang Dai
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, China.
- Peng Cheng Laboratory, Shenzhen, China.
| | - Ming Li
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China.
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, China.
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, China.
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17
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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 2022; 13:5847. [PMID: 36195589 PMCID: PMC9532389 DOI: 10.1038/s41467-022-33441-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2021] [Accepted: 09/19/2022] [Indexed: 11/09/2022] Open
Abstract
Ising machines are a promising non-von-Neumann computational concept for neural network training and combinatorial optimization. However, while various neural networks can be implemented with Ising machines, their inability to perform fast statistical sampling makes them inefficient for training neural networks compared to digital computers. Here, we introduce a universal concept to achieve ultrafast statistical sampling with analog Ising machines by injecting noise. With an opto-electronic Ising machine, we experimentally demonstrate that this can be used for accurate sampling of Boltzmann distributions and for unsupervised training of neural networks, with equal accuracy as software-based training. Through simulations, we find that Ising machines can perform statistical sampling orders-of-magnitudes faster than software-based methods. This enables the use of Ising machines beyond combinatorial optimization and makes them into efficient tools for machine learning and other applications.
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Affiliation(s)
- Fabian Böhm
- Applied Physics Research Group, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium.
| | - Diego Alonso-Urquijo
- Applied Physics Research Group, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium
| | - Guy Verschaffelt
- Applied Physics Research Group, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium
| | - Guy Van der Sande
- Applied Physics Research Group, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium.
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18
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A tree search algorithm towards solving Ising formulated combinatorial optimization problems. Sci Rep 2022; 12:14755. [PMID: 36042250 PMCID: PMC9427840 DOI: 10.1038/s41598-022-19102-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2022] [Accepted: 08/24/2022] [Indexed: 11/12/2022] Open
Abstract
Simulated annealing (SA) attracts more attention among classical heuristic algorithms because many combinatorial optimization problems can be easily recast as the ground state search problem of the Ising Hamiltonian. However, for practical implementation, the annealing process cannot be arbitrarily slow and hence, it may deviate from the expected stationary Boltzmann distribution and become trapped in a local energy minimum. To overcome this problem, this paper proposes a heuristic search algorithm by expanding search space from a Markov chain to a recursive depth limited tree based on SA, where the parent and child nodes represent the current and future spin states. At each iteration, the algorithm selects the best near-optimal solution within the feasible search space by exploring along the tree in the sense of “look ahead”. Furthermore, motivated by the coherent Ising machine (CIM), the discrete representation of spin states is relaxed to a continuous representation with a regularization term, which enables the use of the reduced dynamics of the oscillators to explore the surrounding neighborhood of the selected tree nodes. We tested our algorithm on a representative NP-hard problem (MAX-CUT) to illustrate the effectiveness of the proposed algorithm compared to semi-definite programming (SDP), SA, and simulated CIM. Our results show that with the primal heuristics SA and CIM, our high-level tree search strategy is able to provide solutions within fewer epochs for Ising formulated combinatorial optimization problems.
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19
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Nakajima M, Tanaka K, Hashimoto T. Neural Schrödinger Equation: Physical Law as Deep Neural Network. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:2686-2700. [PMID: 34731081 DOI: 10.1109/tnnls.2021.3120472] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We show a new family of neural networks based on the Schrödinger equation (SE-NET). In this analogy, the trainable weights of the neural networks correspond to the physical quantities of the Schrödinger equation. These physical quantities can be trained using the complex-valued adjoint method. Since the propagation of the SE-NET can be described by the evolution of physical systems, its outputs can be computed by using a physical solver. The trained network is transferable to actual optical systems. As a demonstration, we implemented the SE-NET with the Crank-Nicolson finite difference method on Pytorch. From the results of numerical simulations, we found that the performance of the SE-NET becomes better when the SE-NET becomes wider and deeper. However, the training of the SE-NET was unstable due to gradient explosions when SE-NET becomes deeper. Therefore, we also introduced phase-only training, which only updates the phase of the potential field (refractive index) in the Schrödinger equation. This enables stable training even for the deep SE-NET model because the unitarity of the system is kept under the training. In addition, the SE-NET enables a joint optimization of physical structures and digital neural networks. As a demonstration, we performed a numerical demonstration of end-to-end machine learning (ML) with an optical frontend toward a compact spectrometer. Our results extend the application field of ML to hybrid physical-digital optimizations.
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20
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Liao Z, Ma K, Sarker MS, Tang S, Yamahara H, Seki M, Tabata H. Quantum Analog Annealing of Gain‐Dissipative Ising Machine Driven by Colored Gaussian Noise. ADVANCED THEORY AND SIMULATIONS 2022. [DOI: 10.1002/adts.202100497] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Zhiqiang Liao
- Department of Electrical Engineering and Information Systems Graduate School of Engineering The University of Tokyo Tokyo 113‐8656 Japan
| | - Kaijie Ma
- Department of Bioengineering Graduate School of Engineering The University of Tokyo Tokyo 113‐8656 Japan
| | - Md Shamim Sarker
- Department of Electrical Engineering and Information Systems Graduate School of Engineering The University of Tokyo Tokyo 113‐8656 Japan
| | - Siyi Tang
- Department of Electrical Engineering and Information Systems Graduate School of Engineering The University of Tokyo Tokyo 113‐8656 Japan
| | - Hiroyasu Yamahara
- Department of Electrical Engineering and Information Systems Graduate School of Engineering The University of Tokyo Tokyo 113‐8656 Japan
| | - Munetoshi Seki
- Department of Electrical Engineering and Information Systems Graduate School of Engineering The University of Tokyo Tokyo 113‐8656 Japan
- Center for Spintronics Research Network Graduate School of Engineering The University of Tokyo Tokyo 113‐8656 Japan
| | - Hitoshi Tabata
- Department of Electrical Engineering and Information Systems Graduate School of Engineering The University of Tokyo Tokyo 113‐8656 Japan
- Department of Bioengineering Graduate School of Engineering The University of Tokyo Tokyo 113‐8656 Japan
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21
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Caravelli F, Sheldon FC, Traversa FL. Global minimization via classical tunneling assisted by collective force field formation. SCIENCE ADVANCES 2021; 7:eabh1542. [PMID: 34936465 PMCID: PMC8694608 DOI: 10.1126/sciadv.abh1542] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/19/2021] [Accepted: 11/05/2021] [Indexed: 06/14/2023]
Abstract
Simple elements interacting in networks can give rise to intricate emergent behaviors. Examples such as synchronization and phase transitions often apply in many contexts, as many different systems may reduce to the same effective model. Here, we demonstrate such a behavior in a model inspired by memristors. When weakly driven, the system is described by movement in an effective potential, but when strongly driven, instabilities cause escapes from local minima, which can be interpreted as an unstable tunneling mechanism. We dub this collective and nonperturbative effect a “Lyapunov force,” which steers the system toward the global minimum of the potential function, even if the full system has a constellation of equilibrium points growing exponentially with the system size. This mechanism is appealing for its physical relevance in nanoscale physics and for its possible applications in optimization, Monte Carlo schemes, and machine learning.
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Affiliation(s)
- Francesco Caravelli
- Theoretical Division (T4), Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | - Forrest C. Sheldon
- Theoretical Division (T4), Los Alamos National Laboratory, Los Alamos, NM 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
- London Institute for Mathematical Sciences, 35a South St., London W1K 2XF, UK
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22
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Honjo T, Sonobe T, Inaba K, Inagaki T, Ikuta T, Yamada Y, Kazama T, Enbutsu K, Umeki T, Kasahara R, Kawarabayashi KI, Takesue H. 100,000-spin coherent Ising machine. SCIENCE ADVANCES 2021; 7:eabh0952. [PMID: 34586855 PMCID: PMC8480917 DOI: 10.1126/sciadv.abh0952] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2021] [Accepted: 08/04/2021] [Indexed: 05/20/2023]
Abstract
Computers based on physical systems are increasingly anticipated to overcome the impending limitations on digital computer performance. One such computer is a coherent Ising machine (CIM) for solving combinatorial optimization problems. Here, we report a CIM with 100,512 degenerate optical parametric oscillator pulses working as the Ising spins. We show that the CIM delivers fine solutions to maximum cut problems of 100,000-node graphs drastically faster than standard simulated annealing. Moreover, the CIM, when operated near the phase transition point, provides some extremely good solutions and a very broad distribution. This characteristic will be useful for applications that require fast random sampling such as machine learning.
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Affiliation(s)
- Toshimori Honjo
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
- Corresponding author. (T.H.); (H.T.)
| | - Tomohiro Sonobe
- National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
| | - Kensuke Inaba
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Takahiro Inagaki
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Takuya Ikuta
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Yasuhiro Yamada
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Takushi Kazama
- NTT Device Technology Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Koji Enbutsu
- NTT Device Technology Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Takeshi Umeki
- NTT Device Technology Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Ryoichi Kasahara
- NTT Device Technology Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Ken-ichi Kawarabayashi
- National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
| | - Hiroki Takesue
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
- Corresponding author. (T.H.); (H.T.)
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23
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Fang Y, Huang J, Ruan Z. Experimental Observation of Phase Transitions in Spatial Photonic Ising Machine. PHYSICAL REVIEW LETTERS 2021; 127:043902. [PMID: 34355963 DOI: 10.1103/physrevlett.127.043902] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
Statistical spin dynamics plays a key role in understanding the working principle for novel optical Ising machines. Here, we propose the gauge transformation for a spatial photonic Ising machine, where a single spatial phase modulator simultaneously encodes spin configurations and programs interaction strengths. Using gauge transformation, we experimentally evaluate the phase diagram of a high-dimensional spin-glass equilibrium system with 100 fully connected spins. We observe the presence of paramagnetic, ferromagnetic, and spin-glass phases and determine the critical temperature T_{c} and the critical probability p_{c} of the phase transitions, which agree well with the mean-field theory predictions. Thus, the approximation of the mean-field model is experimentally verified in the spatial photonic Ising machine. Furthermore, we discuss the phase transition in parallel with solving combinatorial optimization problems during the cooling process and identify that the spatial photonic Ising machine is robust with sufficient many-spin interactions even when the system is associated with optical aberrations and measurement uncertainty.
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Affiliation(s)
- Yisheng Fang
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Junyi Huang
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Zhichao Ruan
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
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24
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Li L, Liu H, Huang N, Wang Z. Accuracy-enhanced coherent Ising machine using the quantum adiabatic theorem. OPTICS EXPRESS 2021; 29:18530-18539. [PMID: 34154108 DOI: 10.1364/oe.426476] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Accepted: 05/17/2021] [Indexed: 06/13/2023]
Abstract
The coherent Ising machine (CIM) implemented by degenerate optical parametric oscillator (DOPO) networks is a novel optical platform to accelerate computation of hard combinatorial optimization problems. Nevertheless, with the increase of the problem size, the probability of the machine being trapped by local minima increases exponentially. According to the quantum adiabatic theorem, a physical system will remain in its instantaneous ground state if the time-dependent Hamiltonian varies slowly enough. Here, we propose a method to help the machine partially avoid getting stuck in local minima by introducing quantum adiabatic evolution to the ground-state-search process of the CIM, which we call A-CIM. Numerical simulation results demonstrate that A-CIM can obtain improved solution accuracy in solving MAXCUT problems of vertices ranging from 10 to 2000 than CIM. The proposed machine that is based on quantum adiabatic theorem is expected to solve optimization problems more correctly.
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25
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Marcucci G, Pierangeli D, Conti C. Theory of Neuromorphic Computing by Waves: Machine Learning by Rogue Waves, Dispersive Shocks, and Solitons. PHYSICAL REVIEW LETTERS 2020; 125:093901. [PMID: 32915624 DOI: 10.1103/physrevlett.125.093901] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2019] [Revised: 04/14/2020] [Accepted: 07/09/2020] [Indexed: 06/11/2023]
Abstract
We study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layered model, with an encoding input layer, a wave layer, and a decoding readout, behaves as a conventional neural network in approximating mathematical functions, real-world datasets, and universal Boolean gates. The rank of the transmission matrix has a fundamental role in assessing the learning abilities of the wave. For a given set of training points, a threshold nonlinearity for universal interpolation exists. When considering the nonlinear Schrödinger equation, the use of highly nonlinear regimes implies that solitons, rogue, and shock waves do have a leading role in training and computing. Our results may enable the realization of novel machine learning devices by using diverse physical systems, as nonlinear optics, hydrodynamics, polaritonics, and Bose-Einstein condensates. The application of these concepts to photonics opens the way to a large class of accelerators and new computational paradigms. In complex wave systems, as multimodal fibers, integrated optical circuits, random, topological devices, and metasurfaces, nonlinear waves can be employed to perform computation and solve complex combinatorial optimization.
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Affiliation(s)
- Giulia Marcucci
- Institute for Complex Systems, National Research Council (ISC-CNR), Via dei Taurini 19, 00185 Rome, Italy and Department of Physics, Sapienza University, Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - Davide Pierangeli
- Institute for Complex Systems, National Research Council (ISC-CNR), Via dei Taurini 19, 00185 Rome, Italy and Department of Physics, Sapienza University, Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - Claudio Conti
- Institute for Complex Systems, National Research Council (ISC-CNR), Via dei Taurini 19, 00185 Rome, Italy and Department of Physics, Sapienza University, Piazzale Aldo Moro 2, 00185 Rome, Italy
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26
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Okawachi Y, Yu M, Jang JK, Ji X, Zhao Y, Kim BY, Lipson M, Gaeta AL. Demonstration of chip-based coupled degenerate optical parametric oscillators for realizing a nanophotonic spin-glass. Nat Commun 2020; 11:4119. [PMID: 32807796 PMCID: PMC7431591 DOI: 10.1038/s41467-020-17919-6] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2020] [Accepted: 07/22/2020] [Indexed: 12/04/2022] Open
Abstract
The need for solving optimization problems is prevalent in various physical applications, including neuroscience, network design, biological systems, socio-economics, and chemical reactions. Many of these are classified as non-deterministic polynomial-time hard and thus become intractable to solve as the system scales to a large number of elements. Recent research advances in photonics have sparked interest in using a network of coupled degenerate optical parametric oscillators (DOPOs) to effectively find the ground state of the Ising Hamiltonian, which can be used to solve other combinatorial optimization problems through polynomial-time mapping. Here, using the nanophotonic silicon-nitride platform, we demonstrate a spatial-multiplexed DOPO system using continuous-wave pumping. We experimentally demonstrate the generation and coupling of two microresonator-based DOPOs on a single chip. Through a reconfigurable phase link, we achieve both in-phase and out-of-phase operation, which can be deterministically achieved at a fast regeneration speed of 400 kHz with a large phase tolerance.
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Affiliation(s)
- Yoshitomo Okawachi
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, 10027, USA
| | - Mengjie Yu
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, 10027, USA
- School of Electrical and Computer Engineering, Cornell University, Ithaca, NY, 14853, USA
| | - Jae K Jang
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, 10027, USA
| | - Xingchen Ji
- Department of Electrical Engineering, Columbia University, New York, NY, 10027, USA
| | - Yun Zhao
- Department of Electrical Engineering, Columbia University, New York, NY, 10027, USA
| | - Bok Young Kim
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, 10027, USA
| | - Michal Lipson
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, 10027, USA
- Department of Electrical Engineering, Columbia University, New York, NY, 10027, USA
| | - Alexander L Gaeta
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, 10027, USA.
- Department of Electrical Engineering, Columbia University, New York, NY, 10027, USA.
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27
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Lo HP, Inagaki T, Honjo T, Takesue H. Observation of binary phase states of time-multiplexed degenerate optical parametric oscillator pulses generated using a nonlinear fiber Sagnac loop. OPTICS LETTERS 2020; 45:4503-4506. [PMID: 32796994 DOI: 10.1364/ol.395779] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2020] [Accepted: 07/04/2020] [Indexed: 06/11/2023]
Abstract
We generated time-multiplexed degenerate optical parametric oscillator (DOPO) pulses using a nonlinear fiber Sagnac loop as a phase-sensitive amplifier (PSA), where the pump and amplified light in pump-signal-idler degenerate four-wave mixing can be spatially separated. By placing the PSA in a fiber cavity, we successfully generated more than 5000 time-multiplexed DOPO pulses. We confirmed the bifurcation of pulse phases to 0 or π relative to the pump phase, which makes them useful for representing Ising spins in an Ising model solver based on coherent optical oscillator networks. We also confirmed inherent randomness of the DOPO phases using the National Institute of Standards and Technology random number test.
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28
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Hao T, Cen Q, Guan S, Li W, Dai Y, Zhu N, Li M. Optoelectronic parametric oscillator. LIGHT, SCIENCE & APPLICATIONS 2020; 9:102. [PMID: 32566172 PMCID: PMC7295800 DOI: 10.1038/s41377-020-0337-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2020] [Revised: 05/19/2020] [Accepted: 05/25/2020] [Indexed: 05/25/2023]
Abstract
Oscillators are one of the key elements in various applications as a signal source to generate periodic oscillations. Among them, an optical parametric oscillator (OPO) is a driven harmonic oscillator based on parametric frequency conversion in an optical cavity, which has been widely investigated as a coherent light source with an extremely wide wavelength tuning range. However, steady oscillation in an OPO is confined by the cavity delay, which leads to difficulty in frequency tuning, and the frequency tuning is discrete with the minimum tuning step determined by the cavity delay. Here, we propose and demonstrate a counterpart of an OPO in the optoelectronic domain, i.e., an optoelectronic parametric oscillator (OEPO) based on parametric frequency conversion in an optoelectronic cavity to generate microwave signals. Owing to the unique energy-transition process in the optoelectronic cavity, the phase evolution in the OEPO is not linear, leading to steady single-mode oscillation or multimode oscillation that is not bounded by the cavity delay. Furthermore, the multimode oscillation in the OEPO is stable and easy to realize owing to the phase control of the parametric frequency-conversion process in the optoelectronic cavity, while stable multimode oscillation is difficult to achieve in conventional oscillators such as an optoelectronic oscillator (OEO) or an OPO due to the mode-hopping and mode-competition effect. The proposed OEPO has great potential in applications such as microwave signal generation, oscillator-based computation, and radio-frequency phase-stable transfer.
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Affiliation(s)
- Tengfei Hao
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083 China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, 100049 China
| | - Qizhuang Cen
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, 100876 China
| | - Shanhong Guan
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, 100876 China
| | - Wei Li
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083 China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, 100049 China
| | - Yitang Dai
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, 100876 China
| | - Ninghua Zhu
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083 China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, 100049 China
| | - Ming Li
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083 China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, 100049 China
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Chembo YK. Machine learning based on reservoir computing with time-delayed optoelectronic and photonic systems. CHAOS (WOODBURY, N.Y.) 2020; 30:013111. [PMID: 32013503 DOI: 10.1063/1.5120788] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2019] [Accepted: 11/26/2019] [Indexed: 06/10/2023]
Abstract
The concept of reservoir computing emerged from a specific machine learning paradigm characterized by a three-layered architecture (input, reservoir, and output), where only the output layer is trained and optimized for a particular task. In recent years, this approach has been successfully implemented using various hardware platforms based on optoelectronic and photonic systems with time-delayed feedback. In this review, we provide a survey of the latest advances in this field, with some perspectives related to the relationship between reservoir computing, nonlinear dynamics, and network theory.
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Affiliation(s)
- Yanne K Chembo
- Department of Electrical and Computer Engineering, Institute for Research in Electronics and Applied Physics (IREAP), University of Maryland, 8279 Paint Branch Dr., College Park, Maryland 20742, USA
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