Critical branching processes in digital memcomputing machines

Memcomputing is a novel computing paradigm that employs time non-locality (memory) to solve combinatorial optimization problems. It can be realized in practice by means of non-linear dynamical systems whose point attractors represent the solutions of the original problem. It has been previously shown that during the solution search digital memcomputing machines go through a transient phase of avalanches (instantons) that promote dynamical long-range order. By employing mean-field arguments we predict that the distribution of the avalanche sizes follows a Borel distribution typical of critical branching processes with exponent $\tau= 3/2$. We corroborate this analysis by solving various random 3-SAT instances of the Boolean satisfiability problem. The numerical results indicate a power-law distribution with exponent $\tau = 1.51 \pm 0.02$, in very good agreement with the mean-field analysis. This indicates that memcomputing machines self-tune to a critical state in which avalanches are characterized by a branching process, and that this state persists across the majority of their evolution.Comment: 5 pages, 3 figure

Can biological quantum networks solve NP-hard problems?

There is a widespread view that the human brain is so complex that it cannot be efficiently simulated by universal Turing machines. During the last decades the question has therefore been raised whether we need to consider quantum effects to explain the imagined cognitive power of a conscious mind. This paper presents a personal view of several fields of philosophy and computational neurobiology in an attempt to suggest a realistic picture of how the brain might work as a basis for perception, consciousness and cognition. The purpose is to be able to identify and evaluate instances where quantum effects might play a significant role in cognitive processes. Not surprisingly, the conclusion is that quantum-enhanced cognition and intelligence are very unlikely to be found in biological brains. Quantum effects may certainly influence the functionality of various components and signalling pathways at the molecular level in the brain network, like ion ports, synapses, sensors, and enzymes. This might evidently influence the functionality of some nodes and perhaps even the overall intelligence of the brain network, but hardly give it any dramatically enhanced functionality. So, the conclusion is that biological quantum networks can only approximately solve small instances of NP-hard problems. On the other hand, artificial intelligence and machine learning implemented in complex dynamical systems based on genuine quantum networks can certainly be expected to show enhanced performance and quantum advantage compared with classical networks. Nevertheless, even quantum networks can only be expected to efficiently solve NP-hard problems approximately. In the end it is a question of precision - Nature is approximate.Comment: 38 page

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

Scalable Emulation of Sign-Problem−-Free Hamiltonians with Room Temperature p-bits

The growing field of quantum computing is based on the concept of a q-bit which is a delicate superposition of 0 and 1, requiring cryogenic temperatures for its physical realization along with challenging coherent coupling techniques for entangling them. By contrast, a probabilistic bit or a p-bit is a robust classical entity that fluctuates between 0 and 1, and can be implemented at room temperature using present-day technology. Here, we show that a probabilistic coprocessor built out of room temperature p-bits can be used to accelerate simulations of a special class of quantum many-body systems that are sign-problem$-$free or stoquastic, leveraging the well-known Suzuki-Trotter decomposition that maps a $d$-dimensional quantum many body Hamiltonian to a $d$+1-dimensional classical Hamiltonian. This mapping allows an efficient emulation of a quantum system by classical computers and is commonly used in software to perform Quantum Monte Carlo (QMC) algorithms. By contrast, we show that a compact, embedded MTJ-based coprocessor can serve as a highly efficient hardware-accelerator for such QMC algorithms providing several orders of magnitude improvement in speed compared to optimized CPU implementations. Using realistic device-level SPICE simulations we demonstrate that the correct quantum correlations can be obtained using a classical p-circuit built with existing technology and operating at room temperature. The proposed coprocessor can serve as a tool to study stoquastic quantum many-body systems, overcoming challenges associated with physical quantum annealers.Comment: Fixed minor typos and expanded Appendi

Parallel computing for brain simulation

[Abstract] Background: The human brain is the most complex system in the known universe, it is therefore one of the greatest mysteries. It provides human beings with extraordinary abilities. However, until now it has not been understood yet how and why most of these abilities are produced. Aims: For decades, researchers have been trying to make computers reproduce these abilities, focusing on both understanding the nervous system and, on processing data in a more efficient way than before. Their aim is to make computers process information similarly to the brain. Important technological developments and vast multidisciplinary projects have allowed creating the first simulation with a number of neurons similar to that of a human brain. Conclusion: This paper presents an up-to-date review about the main research projects that are trying to simulate and/or emulate the human brain. They employ different types of computational models using parallel computing: digital models, analog models and hybrid models. This review includes the current applications of these works, as well as future trends. It is focused on various works that look for advanced progress in Neuroscience and still others which seek new discoveries in Computer Science (neuromorphic hardware, machine learning techniques). Their most outstanding characteristics are summarized and the latest advances and future plans are presented. In addition, this review points out the importance of considering not only neurons: Computational models of the brain should also include glial cells, given the proven importance of astrocytes in information processing.Galicia. Consellería de Cultura, Educación e Ordenación Universitaria; GRC2014/049Galicia. Consellería de Cultura, Educación e Ordenación Universitaria; R2014/039Instituto de Salud Carlos III; PI13/0028

Understanding Quantum Technologies 2022

Understanding Quantum Technologies 2022 is a creative-commons ebook that provides a unique 360 degrees overview of quantum technologies from science and technology to geopolitical and societal issues. It covers quantum physics history, quantum physics 101, gate-based quantum computing, quantum computing engineering (including quantum error corrections and quantum computing energetics), quantum computing hardware (all qubit types, including quantum annealing and quantum simulation paradigms, history, science, research, implementation and vendors), quantum enabling technologies (cryogenics, control electronics, photonics, components fabs, raw materials), quantum computing algorithms, software development tools and use cases, unconventional computing (potential alternatives to quantum and classical computing), quantum telecommunications and cryptography, quantum sensing, quantum technologies around the world, quantum technologies societal impact and even quantum fake sciences. The main audience are computer science engineers, developers and IT specialists as well as quantum scientists and students who want to acquire a global view of how quantum technologies work, and particularly quantum computing. This version is an extensive update to the 2021 edition published in October 2021.Comment: 1132 pages, 920 figures, Letter forma