Phase Space Engineering of Digital Memcomputing Machines

Memcomputing machines are dynamical systems that leverage memory (time non-locality) and long-range order to efficiently solve combinatorial optimization problems. In this talk, we discuss how their digital counterparts, Digital Memcomputing Machines (DMMs), navigate high-dimensional phase spaces to reach a global minimum, corresponding to a given problem's logical solution. These dynamics feature instantonic jumps between saddle points of decreasing index. This paradigm is reliant upon the particular timescales present in a DMM, which, in turn, influence the curvature of saddle points' stable and unstable directions. We will then discuss ways to engineer their phase space for optimal performance.