The commercial and industrial demand for the solution of hard combinatorialoptimization problems push forward the development of efficient solvers. One ofthem is the Ising machine which can solve combinatorial problems mapped toIsing Hamiltonians. In particular, spintronic hardware implementations of Isingmachines can be very efficient in terms of area and performance, and arerelatively low-cost considering the potential to create hybrid CMOS-spintronictechnology. Here, we perform a comparison of coherent and probabilisticparadigms of Ising machines on several hard Max-Cut instances, analyzing theirscalability and performance at software level. We show that probabilistic Isingmachines outperform coherent Ising machines in terms of the number ofiterations required to achieve the problem s solution. Nevertheless, highfrequency spintronic oscillators with sub-nanosecond synchronization timescould be very promising as ultrafast Ising machines. In addition, consideringthat a coherent Ising machine acts better for Max-Cut problems because of theabsence of the linear term in the Ising Hamiltonian, we introduce a procedureto encode Max-3SAT to Max-Cut. We foresee potential synergic interplays betweenthe two paradigms.
The primary objective of this paper is to present an exact and generalprocedure for mapping any sequence of quantum gates onto a network ofprobabilistic p-bits which can take on one of two values 0 and 1. The first $n$p-bits represent the input qubits, while the other p-bits represent the qubitsafter the application of successive gating operations. We can view thisstructure as a Boltzmann machine whose states each represent a Feynman pathleading from an initial configuration of qubits to a final configuration. Eachsuch path has a complex amplitude $\psi$ which can be associated with a complexenergy. The real part of this energy can be used to generate samples of Feynmanpaths in the usual way, while the imaginary part is accounted for by treatingthe samples as complex entities, unlike ordinary Boltzmann machines wheresamples are positive. Quantum gates often have purely imaginary energyfunctions for which all configurations have the same probability and one cannottake advantage of sampling techniques. However, if we can use suitabletransformations to introduce a real part in the energy function then powerfulsampling algorithms like Gibbs sampling can be harnessed to get acceptableresults with far fewer samples and perhaps even escape the exponential scalingwith $nd$. This algorithmic acceleration can then be supplemented withspecial-purpose hardware accelerators like Ising Machines which can obtain avery large number of samples per second through a combination of massiveparallelism, pipelining, and clockless mixed-signal operation made possible bycodesigning circuits and architectures to match the algorithm. Our results formapping an arbitrary quantum circuit to a Boltzmann machine with a complexenergy function should help push the boundaries of the simulability of quantumcircuits with probabilistic resources and compare them with NISQ-era quantumcomputers.
The slowing down of Moore’s Law has led to a crisis as the computing workloads of Artificial Intelligence (AI) algorithms continue skyrocketing. There is an urgent need for scalable and energy-efficient hardware catering to the unique requirements of AI algorithms and applications. In this environment, probabilistic computing with p-bits emerged as a scalable, domain-specific, and energy-efficient computing paradigm, particularly useful for probabilistic applications and algorithms.In particular, spintronic devices such as stochastic magnetic tunnel junctions (sMTJ) show great promise in designing integrated p-computers. Here, we examine how a scalable probabilistic computer with such magnetic p-bits can be useful for an emerging field combining machine learning and quantum physics.
The transistor celebrated its 75th birthday in 2022. The continued scaling of the transistor defined by Moore’s law continues, albeit at a slower pace. Meanwhile, computing demands and energy consumption required by modern artificial intelligence (AI) algorithms have skyrocketed. As an alternative to scaling transistors for general-purpose computing, the integration of transistors with unconventional technologies has emerged as a promising path for domain-specific computing. In this article, we provide a full-stack review of probabilistic computing with p-bits as a representative example of the energy-efficient and domain-specific computing movement. We argue that p-bits could be used to build energy-efficient probabilistic systems, tailored for probabilistic algorithms and applications. From hardware, architecture, and algorithmic perspectives, we outline the main applications of probabilistic computers ranging from probabilistic machine learning (ML) and AI to combinatorial optimization and quantum simulation. Combining emerging nanodevices with the existing CMOS ecosystem will lead to probabilistic computers with orders of magnitude improvements in energy efficiency and probabilistic sampling, potentially unlocking previously unexplored regimes for powerful probabilistic algorithms.
There is an emerging industrial demand for predictive maintenance algorithms that exhibit high levels of predictive accuracy. Such condition monitoring tools must estimate dynamic quantities, such as Remaining Useful Lifetime (RUL) and the State of Health (SOH), based on a, typically, restricted set of measurements that can be obtained in an operational setting. These quantities exhibit inherent stochasticity and can only be approximately determined a posteriori to system failure. This paper proposes a generic prognostic tool for probabilistic condition monitoring of mechatronic systems, with the aim to improve the probabilistic prediction of condition metrics, specifically RUL and SOH. Therefore we propose to identify a Hidden Markov Model (HMM) from a fully instrumented measurement set, that is only available for a restricted set of run-to-failure experiments, typically gathered in an R&D setting. Although being artificial and retrospectively constructed metrics, we interpret RUL and SOH as physical measurements with the purpose to identify accurate degradation dynamics. Once the degradation model is identified, we practice the mathematical flexibility of the HMM framework to estimate several of the no longer available dynamic quantities of interest in real-time, from the limited set of measurements that are available in an operational setting. This modelling paradigm is known as virtual sensing. Predictive performance and computational efficiency are further improved by domain knowledge based pre-processing of the measurements. We apply our methodology to solenoid valves (SV), a widely used and often critical component in many industrial systems, which display a large variation in useful lifetime. Benchmark results show that the predictive capabilities of the presented methodology compares with prognostic techniques that are more computationally and memory demanding. Note to Practitioners—The motivation for this research is twofold. First there is a pending industrial need for improved diagnostic and prognostic tools. Second there is the observation that lifetime tests usually take place in an R&D setting and that expert labelling of Remaining Useful Lifetime (RUL) or State of Health (SOH) of a component or system is often based on measurement data that is not available in the industrial setting where the prognostic tools are to be deployed in the end. These two observations suggest that there is large potential in methods that can correlate the expert labelling, in particular RUL & SOH signals, with measurement data that is available in the industrial setting. Our approach has been tested in detail on the case of Solenoid Valves, which are widely used in industry and that are often safety critical. Our experiments demonstrate that the method compares with brute force approaches that overpower ours both in terms of computational as well as memory requirements. The method is furthermore generic and there is no reason to assume it would not work for other applications.