UC San Diego

The evolution of computing technologies has perpetually intersected with the fundamental principles of physics. In this dissertation, we explore the frontier of computational paradigms through the lens of memory-augmented physical systems. Conventional computing, constrained by the architecture of Turing machines, can be substantially evolved by incorporating elements of memory into the physical computing substrates.

We demonstrate that time non-local interactions, conceptualized as "memory," can induce spatial long-range order by correlating distant computational units despite their spatially local interactions. Such long-range order is critical for solving complex optimization problems as it enables strategies that transcend local moves to escape local minima. MemComputing, embodying this methodology, solves target problems by following the trajectory of a dynamical system embedded with memory. This system is meticulously designed so that its equilibrium points align with the solutions of the problem, and it explores distant configurations through instantonic tunneling.

We provide a comprehensive demonstration of the MemComputing framework through applications in complex problem-solving scenarios, including the efficient simulation of quantum systems and tackling NP-complete problems like the SAT problem. Our findings indicate significant enhancements over traditional computing methods, spotlighting the profound potential of integrating memory with physical systems for next-generation computing.

This research not only deepens our understanding of the intersection between memory and physical laws in computational processes but also establishes a foundational basis for the development of next-generation computing technologies. These technologies are poised to be more efficient, scalable, and aligned with natural dynamical processes, representing a significant leap over conventional computational frameworks.