Phase-space engineering and collective dynamics in memcomputing
Phys. Rev. Applied 25, 014048 – Published 21 January, 2026
DOI: https://doi.org/10.1103/f8tv-jv1b
Abstract
This paper is a contribution to the Physical Review Applied collection titled Physics-Inspired Computing.
Digital memcomputing machines (DMMs) are dynamical systems with memory (time nonlocality) that have been designed to solve combinatorial optimization problems. Their corresponding ordinary differential equations depend on a few hyperparameters that define both the system’s relevant timescales and its phase-space geometry. Using numerical simulations on a prototypical DMM, we analyze the role of these physical parameters in engineering the phase space to either help or hinder the solution search by DMMs. We find that the DMM explores its phase space efficiently for a wide range of parameters, aided by the system-wide correlations in their fast degrees of freedom that emerge dynamically due to coupling with the (slow) memory degrees of freedom. In this regime, the time it takes for the system to find a solution scales well as the number of variables increases. When these hyperparameters are chosen poorly, the system navigates its phase space far less efficiently. However, we find that, in many cases, collective behavior persists even when the phase-space exploration process is inefficient. This behavior only disappears if the memories are made to evolve as quickly as the fast degrees of freedom. This study points to the important role of memory and hyperparameters in engineering the DMMs’ phase space for optimal computational efficiency.
Physics Subject Headings (PhySH)
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This article appears in the following collection:
Collection on Physics-Inspired Computing
Physical Review Applied is pleased to present a Collection on Physics-Inspired Computing, highlighting the rapidly evolving field of energy-efficient computing techniques, from hardware technologies to algorithms, where physics inspiration serves as the crucial link. Contributions to this collection will be published throughout 2025. This Collection is being curated by Guest Editors Kerem Camsari and Supriyo Datta.
