Which features make the brain such a powerful and energy-efficient computing machine? Can we reproduce them in the solid state, and if so, what type of computing paradigm would we obtain? I will show that a machine that uses memory to both process and store information, like our brain, and is endowed with intrinsic parallelism and information overhead - namely takes advantage, via its collective state, of the network topology related to the problem - has a computational power far beyond our standard digital computers . We have named this novel computing paradigm “memcomputing” [2, 3]. As an example, I will show the polynomial-time solution of prime factorization, the search version of the subset-sum problem and the Max-SAT using polynomial resources and self-organizing logic gates, namely gates that self-organize to satisfy their logical proposition . I will also demonstrate that these machines are described by a topological field theory and they compute via an instantonic phase, implying that they are robust against noise and disorder . The digital memcomputing machines that we propose can also be efficiently simulated, are scalable and can be easily realized with available nanotechnology components, and may help reveal aspects of computation of the brain.
 F. L. Traversa and M. Di Ventra, Universal Memcomputing Machines, IEEE Transactions on Neural Networks and Learning Systems 26, 2702 (2015).
 M. Di Ventra and Y.V. Pershin, Computing: the Parallel Approach, Nature Physics 9, 200 (2013).
 M. Di Ventra and Y.V. Pershin, Just add memory, Scientific American 312, 56 (2015).
 F. L. Traversa and M. Di Ventra, Polynomial-time solution of prime factorization and NP-complete problems with digital memcomputing machines, Chaos: An Interdisciplinary Journal of Nonlinear Science 27, 023107 (2017).
 M. Di Ventra, F. L. Traversa and I.V. Ovchinnikov, Topological field theory and computing with instantons, Annalen der Physik 1700123 (2017).
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 has been Visiting Scientist at IBM T.J. Watson Research Center and Research Assistant Professor at Vanderbilt University before joining the Physics Department of Virginia Tech in 2000 as Assistant Professor. He was promoted to Associate Professor in 2003 and moved to the Physics Department of the University of California, San Diego, in 2004 where he was promoted to Full Professor in 2006.
Di Ventra's research interests are in the theory of electronic and transport properties of 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 has been invited to deliver more than 270 talks worldwide on these topics (including 12 plenary/keynote presentations, 9 talks at the March Meeting of the American Physical Society, 5 at the Materials Research Society, 2 at the American Chemical Society, and 2 at the SPIE).
He has been Visiting Professor at the Technical University of Dresden (2015), University Paris-Sud (2015), Technical University of Denmark (2014), Ben-Gurion University (2013), Scuola Normale Superiore di Pisa (2012, 2011), and SISSA, Trieste (2012). He serves on the editorial board of several scientific journals and has won numerous awards and honors, including the NSF Early CAREER Award, the Ralph E. Powe Junior Faculty Enhancement Award, fellowship in the Institute of Physics and the American Physical Society.
Di Ventra has published more than 200 papers in refereed journals, co-edited the textbook Introduction to Nanoscale Science and Technology (Springer, 2004) for undergraduate students, and he is single author of the graduate-level textbook Electrical Transport in Nanoscale Systems (Cambridge University Press, 2008).