Taming a non-convex landscape with dynamical long-range order: memcomputing Ising benchmarks

Abstract

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.

References in corpus (21)

• Emergent complex neural dynamics
• Theory of Quantum Annealing of an Ising Spin Glass
• What is the Computational Value of Finite Range Tunneling?
• Demonstration of a scaling advantage for a quantum annealer over simulated annealing
• Probing for quantum speedup in spin glass problems with planted solutions
• Universal Memcomputing Machines
• A Cluster Monte Carlo Algorithm for 2-Dimensional Spin Glasses
• The statistics of critical points of Gaussian fields on large-dimensional spaces
• Optimization hardness as transient chaos in an analog approach to constraint satisfaction
• Efficient Cluster Algorithm for Spin Glasses in Any Space Dimension
• Memcomputing: Leveraging memory and physics to compute efficiently
• Seeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly
• Comparing Monte Carlo methods for finding ground states of Ising spin glasses: population annealing, simulated annealing and parallel tempering
• Polynomial-time solution of prime factorization and NP-hard problems with digital memcomputing machines
• Topological field theory and computing with instantons
• The complex dynamics of memristive circuits: analytical results and universal slow relaxation
• Digital Memcomputing: from Logic to Dynamics to Topology
• Critical branching processes in digital memcomputing machines
• Phase Transitions and Duality in Adiabatic Memristive Networks
• MemComputing Integer Linear Programming
• A mean-field model of memristive circuit interaction

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• Mode-Assisted Unsupervised Learning of Restricted Boltzmann Machines
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• Generating Weighted MAX-2-SAT Instances of Tunable Difficulty with Frustrated Loops
• Disorder-assisted graph coloring on quantum annealers
• Non-equilibrium criticality and efficient exploration of glassy landscapes with memory dynamics
• Projective Embedding of Dynamical Systems: uniform mean field equations
• Memcomputing for Accelerated Optimization
• Edge-of-chaos enhanced quantum-inspired algorithm for combinatorial optimization
• Direct comparison of stochastic driven nonlinear dynamical systems for combinatorial optimization