Nanomagnetic Self-Organizing Logic Gates

The end of Moore's law for CMOS technology has prompted the search for low-power computing alternatives, resulting in several promising proposals based on magnetic logic[1-8]. One approach aims at tailoring arrays of nanomagnetic islands in which the magnetostatic interactions constrain the equilibrium orientation of the magnetization to embed logical functionalities[9-12]. Despite the realization of several proofs of concepts of such nanomagnetic logic[13-15], it is still unclear what the advantages are compared to the widespread CMOS designs, due to their need for clocking[16, 17] and/or thermal annealing [18,19] for which fast convergence to the ground state is not guaranteed. In fact, it seems increasingly evident that "beyond CMOS" technology will require a fundamental rethinking of our computing paradigm[20]. In this respect, a type of terminal-agnostic logic was suggested[21], where a given gate is able to "self-organize" into its correct logical states, regardless of whether the signal is applied to the traditional input terminals, or the output terminals. Here, we introduce nanomagnetic self-organizing balanced logic gates, that employ stray-field coupled nanomagnetic islands to perform terminal-agnostic logic. We illustrate their capabilities by implementing reversible Boolean circuitry to solve a two-bit factorization problem via numerical modelling. In view of their design and mode of operation, we expect these systems to improve significantly over those suggested in Ref.[21], thus offering an alternative path to explore memcomputing, whose usefulness has already been demonstrated by solving a variety of hard combinatorial optimization problems[22]

Self-Averaging of Digital MemComputing Machines

Digital MemComputing machines (DMMs) are a new class of computing machines that employ non-quantum dynamical systems with memory to solve combinatorial optimization problems. Here, we show that the time to solution (TTS) of DMMs follows an inverse Gaussian distribution, with the TTS self-averaging with increasing problem size, irrespective of the problem they solve. We provide both an analytical understanding of this phenomenon and numerical evidence by solving instances of the 3-SAT (satisfiability) problem. The self-averaging property of DMMs with problem size implies that they are increasingly insensitive to the detailed features of the instances they solve. This is in sharp contrast to traditional algorithms applied to the same problems, illustrating another advantage of this physics-based approach to computation.Comment: 9 pages, 13 figure

Spatial-photonic Boltzmann machines: low-rank combinatorial optimization and statistical learning by spatial light modulation

The spatial-photonic Ising machine (SPIM) [D. Pierangeli et al., Phys. Rev. Lett. 122, 213902 (2019)] is a promising optical architecture utilizing spatial light modulation for solving large-scale combinatorial optimization problems efficiently. However, the SPIM can accommodate Ising problems with only rank-one interaction matrices, which limits its applicability to various real-world problems. In this Letter, we propose a new computing model for the SPIM that can accommodate any Ising problem without changing its optical implementation. The proposed model is particularly efficient for Ising problems with low-rank interaction matrices, such as knapsack problems. Moreover, the model acquires learning ability and can thus be termed a spatial-photonic Boltzmann machine (SPBM). We demonstrate that learning, classification, and sampling of the MNIST handwritten digit images are achieved efficiently using SPBMs with low-rank interactions. Thus, the proposed SPBM model exhibits higher practical applicability to various problems of combinatorial optimization and statistical learning, without losing the scalability inherent in the SPIM architecture.Comment: 7 pages, 5 figures (with a 3-page supplemental