BRIM: Bistable Resistively-Coupled Ising Machine

Afoakwa, Richard; Zhang, Yiqiao; Vengalam, Uday Kumar Reddy; Ignjatović, Željko; Huang, Michael C.

doi:10.1109/hpca51647.2021.00068

Cited by 36 publications

(21 citation statements)

References 26 publications

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“…91 it was found that for k = 2 the scheme is able to correctly find solutions, but for the more difficult k = 3 case the scheme only succeeded for a subset of problem instances. This approach was theoretically further developed, including explicitly extending to the case of solving Ising problems and analyzing various possible physical implementations [93][94][95][96][97][98] . Oscillator networks have been experimentally demonstrated with various systems such as bulk analog electronic 95,[99][100][101] , VO 2 insulator-to-metal transition 31,102,103 (Fig.…”

Section: Oscillator-based Computingmentioning

confidence: 99%

Ising machines as hardware solvers of combinatorial optimization problems

Mohseni¹,

McMahon²,

Byrnes³

2022

Preprint

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Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity class NP as an Ising problem with only polynomial overhead. A scalable Ising machine that outperforms existing standard digital computers could have a huge impact for practical applications for a wide variety of optimization problems. In this review, we survey the current status of various approaches to constructing Ising machines and explain their underlying operational principles. The types of Ising machines considered here include classical thermal annealers based on technologies such as spintronics, optics, memristors, and digital hardware accelerators; dynamical-systems solvers implemented with optics and electronics; and superconducting-circuit quantum annealers. We compare and contrast their performance using standard metrics such as the ground-state success probability and time-to-solution, give their scaling relations with problem size, and discuss their strengths and weaknesses. Key points• Dedicated hardware solvers for the Ising model are of great interest due to the many potential practical applications and the end of Moore's law which motivate alternative computational approaches.• Three main computing methods that Ising machines employ are classical annealing, quantum annealing, and dynamical system evolution. A single machine can operate based on multiple computing approaches.• Today, Ising hardware based on classical digital technologies are the best performing for common benchmark problems. However, the performance is problem dependent and alternative methods can perform well for particular classes of problems.• For particular crafted problem instances, quantum approaches have been observed to have a superior performance over classical algorithms, motivating quantum hardware approaches and quantum-inspired classical algorithms.• Hybrid quantum-classical and digital-analog algorithms are promising for future development; they may harness the complementary advantages of both.

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Section: Oscillator-based Computingmentioning

confidence: 99%

Ising machines as hardware solvers of combinatorial optimization problems

Mohseni¹,

McMahon²,

Byrnes³

2022

Preprint

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“…(1) Identify the physical variable to represent a spin (be it a qubit [27], the phase of an optical pulse [28], or the polarity of a capacitor [3]); (2) Identify the mechanism of coupling and how to program the coefficients; (3) Demonstrate the problem solving capability showing both the theory of its operation (reveal the "invisible hand" of nature) and satisfactory results of practice; (4) Demonstrate superior machine metrics (solution time, energy consumption, and construction costs).…”

Section: Background and Related Work 21 Principles Of Ising Machinesmentioning

confidence: 99%

Increasing ising machine capacity with multi-chip architectures

Sharma

Afoakwa

Ignjatović

et al. 2022

Proceedings of the 49th Annual International Symposium on Computer Architecture

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Nature has inspired a lot of problem solving techniques over the decades. More recently, researchers have increasingly turned to harnessing nature to solve problems directly. Ising machines are a good example and there are numerous research prototypes as well as many design concepts. They can map a family of NP-complete problems and derive competitive solutions at speeds much greater than conventional algorithms and in some cases, at a fraction of the energy cost of a von Neumann computer.However, physical Ising machines are often fixed in its problem solving capacity. Without any support, a bigger problem cannot be solved at all. With a simple divide-and-conquer strategy, it turns out, the advantage of using an Ising machine quickly diminishes. It is therefore desirable for Ising machines to have a scalable architecture where multiple instances can collaborate to solve a bigger problem. We then discuss scalable architecture design issues which lead to a multiprocessor Ising machine architecture. Experimental analyses show that our proposed architectures allow an Ising machine to scale in capacity and maintain its significant performance advantage (about 2200x speedup over a state-of-the-art computational substrate). In the case of communication bandwidth-limited systems, our proposed optimizations in supporting batch mode operation can cut down communication demand by about 4-5x without a significant impact on solution quality. CCS CONCEPTS• Computer systems organization → Analog computers.

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“…Recently, a new generation of Ising machines based on continuous dynamics has emerged [15][16][17][18][19][20][21][22][23][24]. These machines do not attempt to represent the binary states of the classical spin.…”

Section: Introductionmentioning

confidence: 99%

Scalable almost-linear dynamical Ising machines

Shukla¹,

Erementchouk²,

Mazumder³

2022

Preprint

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The past decade has seen the emergence of Ising machines targeting hard combinatorial optimization problems by minimizing the Ising Hamiltonian with spins represented by continuous dynamical variables. However, capabilities of these machines at larger scales are yet to be fully explored. We investigate an Ising machine based on a network of almost-linearly coupled analog spins. We show that such networks leverage the computational resource similar to that of the semidefinite positive relaxation of the Ising model. We estimate the expected performance of the almost-linear machine and benchmark it on a set of {0, 1}-weighted graphs. We show that the running time of the investigated machine scales polynomially (linearly with the number of edges in the connectivity graph). As an example of the physical realization of the machine, we present a CMOS-compatible implementation comprising an array of vertices efficiently storing the continuous spins on charged capacitors and communicating externally via analog current.

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BRIM: Bistable Resistively-Coupled Ising Machine

Cited by 36 publications

References 26 publications

Ising machines as hardware solvers of combinatorial optimization problems

Ising machines as hardware solvers of combinatorial optimization problems

Increasing ising machine capacity with multi-chip architectures

Scalable almost-linear dynamical Ising machines

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