In the ‘Beyond Moore’s Law’ era, with increasing edge intelligence, domain-specific computing embracing unconventional approaches will become increasingly prevalent. At the same time, adopting a variety of nanotechnologies will offer benefits in energy cost, computational speed, reduced footprint, cyber resilience, and processing power. The time is ripe for a roadmap for unconventional computing with nanotechnologies to guide future research, and this collection aims to fill that need. The authors provide a comprehensive roadmap for neuromorphic computing using electron spins, memristive devices, two-dimensional nanomaterials, nanomagnets, and various dynamical systems. They also address other paradigms such as Ising machines, Bayesian inference engines, probabilistic computing with p-bits, processing in memory, quantum memories and algorithms, computing with skyrmions and spin waves, and brain-inspired computing for incremental learning and problem-solving in severely resource-constrained environments. These approaches have advantages over traditional Boolean computing based on von Neumann architecture. As the computational requirements for artificial intelligence grow 50 times faster than Moore’s Law for electronics, more unconventional approaches to computing and signal processing will appear on the horizon, and this roadmap will help identify future needs and challenges. In a very fertile field, experts in the field aim to present some of the dominant and most promising technologies for unconventional computing that will be around for some time to come. Within a holistic approach, the goal is to provide pathways for solidifying the field and guiding future impactful discoveries.
This content will become publicly available on December 1, 2024
Designing Ising machines with higher order spin interactions and their application in solving combinatorial optimization
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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- Award ID(s):
- 2132918
- NSF-PAR ID:
- 10434158
- Date Published:
- Journal Name:
- Scientific Reports
- Volume:
- 13
- Issue:
- 1
- ISSN:
- 2045-2322
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract -
In the Beyond Moore Law era, with increasing edge intelligence, domain-specific computing embracing unconventional approaches will become increasingly prevalent. At the same time, the adoption of a wide variety of nanotechnologies will offer benefits in energy cost, computational speed, reduced footprint, cyber-resilience and processing prowess. The time is ripe to lay out a roadmap for unconventional computing with nanotechnologies to guide future research and this collection aims to fulfill that need. The authors provide a comprehensive roadmap for neuromorphic computing with electron spins, memristive devices, two-dimensional nanomaterials, nanomagnets and assorted dynamical systems. They also address other paradigms such as Ising machines, Bayesian inference engines, probabilistic computing with p-bits, processing in memory, quantum memories and algorithms, computing with skyrmions and spin waves, and brain inspired computing for incremental learning and solving problems in severely resource constrained environments. All of these approaches have advantages over conventional Boolean computing predicated on the von-Neumann architecture. With the computational need for artificial intelligence growing at a rate 50x faster than Moore law for electronics, more unconventional approaches to computing and signal processing will appear on the horizon and this roadmap will aid in identifying future needs and challenges.more » « less
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Abstract A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order interactions although important classes of optimization problems, such as satisfiability problems, map more seamlessly to Ising networks with higher-order interactions. Here, we demonstrate that higher-order Ising machines can solve satisfiability problems more resource-efficiently in terms of the number of spin variables and their connections when compared to traditional second-order Ising machines. Further, our results show on a benchmark dataset of Boolean
k -satisfiability problems that higher-order Ising machines implemented with coupled oscillators rapidly find solutions that are better than second-order Ising machines, thus, improving the current state-of-the-art for Ising machines. -
null (Ed.)Abstract The transfer of information between quantum systems is essential for quantum communication and computation. In quantum computers, high connectivity between qubits can improve the efficiency of algorithms, assist in error correction, and enable high-fidelity readout. However, as with all quantum gates, operations to transfer information between qubits can suffer from errors associated with spurious interactions and disorder between qubits, among other things. Here, we harness interactions and disorder between qubits to improve a swap operation for spin eigenstates in semiconductor gate-defined quantum-dot spins. We use a system of four electron spins, which we configure as two exchange-coupled singlet–triplet qubits. Our approach, which relies on the physics underlying discrete time crystals, enhances the quality factor of spin-eigenstate swaps by up to an order of magnitude. Our results show how interactions and disorder in multi-qubit systems can stabilize non-trivial quantum operations and suggest potential uses for non-equilibrium quantum phenomena, like time crystals, in quantum information processing applications. Our results also confirm the long-predicted emergence of effective Ising interactions between exchange-coupled singlet–triplet qubits.more » « less
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Abstract The $p$-tensor Ising model is a one-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic is a multi-linear form of degree $p \geqslant 2$. This is a natural generalization of the matrix Ising model that provides a convenient mathematical framework for capturing, not just pairwise, but higher-order dependencies in complex relational data. In this paper, we consider the problem of estimating the natural parameter of the $p$-tensor Ising model given a single sample from the distribution on $N$ nodes. Our estimate is based on the maximum pseudolikelihood (MPL) method, which provides a computationally efficient algorithm for estimating the parameter that avoids computing the intractable partition function. We derive general conditions under which the MPL estimate is $\sqrt N$-consistent, that is, it converges to the true parameter at rate $1/\sqrt N$. Our conditions are robust enough to handle a variety of commonly used tensor Ising models, including spin glass models with random interactions and models where the rate of estimation undergoes a phase transition. In particular, this includes results on $\sqrt N$-consistency of the MPL estimate in the well-known $p$-spin Sherrington–Kirkpatrick model, spin systems on general $p$-uniform hypergraphs and Ising models on the hypergraph stochastic block model (HSBM). In fact, for the HSBM we pin down the exact location of the phase transition threshold, which is determined by the positivity of a certain mean-field variational problem, such that above this threshold the MPL estimate is $\sqrt N$-consistent, whereas below the threshold no estimator is consistent. Finally, we derive the precise fluctuations of the MPL estimate in the special case of the $p$-tensor Curie–Weiss model, which is the Ising model on the complete $p$-uniform hypergraph. An interesting consequence of our results is that the MPL estimate in the Curie–Weiss model saturates the Cramer–Rao lower bound at all points above the estimation threshold, that is, the MPL estimate incurs no loss in asymptotic statistical efficiency in the estimability regime, even though it is obtained by minimizing only an approximation of the true likelihood function for computational tractability.more » « less
