11 research outputs found
Taming a non-convex landscape with dynamical long-range order: memcomputing Ising benchmarks
Recent work on quantum annealing has emphasized the role of collective
behavior in solving optimization problems. By enabling transitions of clusters
of variables, such solvers are able to navigate their state space and locate
solutions more efficiently despite having only local connections between
elements. However, collective behavior is not exclusive to quantum annealers,
and classical solvers that display collective dynamics should also possess an
advantage in navigating a non-convex landscape. Here, we give evidence that a
benchmark derived from quantum annealing studies is solvable in polynomial time
using digital memcomputing machines, which utilize a collection of dynamical
components with memory to represent the structure of the underlying
optimization problem. To illustrate the role of memory and clarify the
structure of these solvers we propose a simple model of these machines that
demonstrates the emergence of long-range order. This model, when applied to
finding the ground state of the Ising frustrated-loop benchmarks, undergoes a
transient phase of avalanches which can span the entire lattice and
demonstrates a connection between long-range behavior and their probability of
success. These results establish the advantages of computational approaches
based on collective dynamics of continuous dynamical systems
MemComputing Integer Linear Programming
Integer linear programming (ILP) encompasses a very important class of
optimization problems that are of great interest to both academia and industry.
Several algorithms are available that attempt to explore the solution space of
this class efficiently, while requiring a reasonable compute time. However,
although these algorithms have reached various degrees of success over the
years, they still face considerable challenges when confronted with
particularly hard problem instances, such as those of the MIPLIB 2010 library.
In this work we propose a radically different non-algorithmic approach to ILP
based on a novel physics-inspired computing paradigm: Memcomputing. This
paradigm is based on digital (hence scalable) machines represented by
appropriate electrical circuits with memory. These machines can be either built
in hardware or, as we do here, their equations of motion can be efficiently
simulated on our traditional computers. We first describe a new circuit
architecture of memcomputing machines specifically designed to solve for the
linear inequalities representing a general ILP problem. We call these
self-organizing algebraic circuits, since they self-organize dynamically to
satisfy the correct (algebraic) linear inequalities. We then show simulations
of these machines using MATLAB running on a single core of a Xeon processor for
several ILP benchmark problems taken from the MIPLIB 2010 library, and compare
our results against a renowned commercial solver. We show that our approach is
very efficient when dealing with these hard problems. In particular, we find
within minutes feasible solutions for one of these hard problems (f2000 from
MIPLIB 2010) whose feasibility, to the best of our knowledge, has remained
unknown for the past eight years
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
Shortest path computing in directed graphs with weighted edges mapped on random networks of memristors
Electronic version of an article published as [Fernandez, Carlos, Ioannis Vourkas, and Antonio Rubio. "Shortest Path Computing in Directed Graphs with Weighted Edges Mapped on Random Networks of Memristors." Parallel Processing Letters 30.01 (2020): 2050002] [https://doi.org/10.1142/S0129626420500024] © [copyright World Scientific Publishing Company] [https://www.worldscientific.com/worldscinet/ppl]To accelerate the execution of advanced computing tasks, in-memory computing with resistive memory provides a promising solution. In this context, networks of memristors could be used as parallel computing medium for the solution of complex optimization problems. Lately, the solution of the shortest-path problem (SPP) in a two-dimensional memristive grid has been given wide consideration. Some still open problems in such computing approach concern the time required for the grid to reach to a steady state, and the time required to read the result, stored in the state of a subset of memristors that represent the solution. This paper presents a circuit simulation-based performance assessment of memristor networks as SPP solvers. A previous methodology was extended to support weighted directed graphs. We tried memristor device models with fundamentally different switching behavior to check their suitability for such applications and the impact on the timely detection of the solution. Furthermore, the requirement of binary vs. analog operation of memristors was evaluated. Finally, the memristor network-based computing approach was compared to known algorithmic solutions to the SPP over a large set of random graphs of different sizes and topologies. Our results contribute to the proper development of bio-inspired memristor network-based SPP solvers.This work was supported by the Chilean research grants CONICYT REDES ETAPA INICIAL Convocatoria 2017 No. REDI170604, CONICYT BASAL FB0008, and by the Spanish MINECO and ERDF (TEC2016-75151-C3-2-R).Peer ReviewedPostprint (author's final draft
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