It is well known that physical phenomena may be of great help in computing some difficult problems efficiently. A typical example is prime factorization that may be solved in polynomial time by exploiting quantum entanglement on a quantum computer. There are, however, other types of (non-quantum) physical properties that one may leverage to compute efficiently a wide range of hard problems. In this talk, I will discuss how to employ one such property, memory (time non-locality), in a novel physics-based approach to computation: Memcomputing. As examples, I will show the polynomial-time solution of prime factorization, the search version of the subset-sum problem, and approximations to the Max-SAT beyond the inapproximability gap using polynomial resources and self-organizing logic gates, namely gates that self-organize to satisfy their logical proposition. I will also show that these machines are robust against noise and disorder. The digital memcomputing machines we propose can be efficiently simulated, are scalable and can be easily realized with available nanotechnology components. Work supported in part by MemComputing, Inc. (http://memcpu.com/) and CMRR.

Massimiliano Di Ventra obtained his undergraduate degree in Physics summa cum laude from the University of Trieste (Italy) in 1991 and did his PhD studies at the Ecole Polytechnique Federale de Lausanne (Switzerland) in 1993-1997. He is now professor of Physics at the University of Californian, San Diego. Di Ventra's research interests are in the theory of quantum transport in nanoscale systems, non-equilibrium statistical mechanics, DNA sequencing/polymer dynamics in nanopores, and memory effects in nanostructures for applications in unconventional computing and biophysics. He is the author of more than 200 scientific publications, three textbooks, and holds four U.S. patents. He has delivered more than 300 invited talks worldwide on his research.