What is in Common Between Quantum Computer and Solar System?

A Google TechTalk, 10/21/16, presented by Boris Altshuler. ABSTRACT: Quantum Computers (QC) consist of a large number of interacting quantum bits. Solutions of computational problems are encoded in bit-strings which result from problem-specific manipulations. In contrast with Classical Computers, the state of a QC is characterized by a quantum superposition of the bit-strings (a wave function) rather than by a particular bit-string representing a computational basis. Instead of usual focus on quantum algorithms, here we will discuss QC using concepts from many-body physics as quantum dynamical systems. Recent progress in understanding the dynamics of quantum systems with large number of degrees of freedom is based on the concept of Many-Body Localization: the eigenstates can be localized in the Hilbert space in a way similar to the conventional real space Anderson Localization of a single quantum particle by a quenched disorder. Depending on the temperature (total energy) or other tunable parameters the system can find itself either in the localized or in the many-body extended phase. In the former case, the system of interacting quantum particles/spins cannot be described in terms of conventional Statistical Mechanics: the notion of the thermal equilibrium loses its meaning. Moreover the violation of the conventional thermodynamics does not disappear with the Anderson transition to an extended state. In a finite range of the tunable parameters we expect the non-ergodic extended phase: the many-body wave-functions being extended are multifractal in the Hilbert space making thermal equilibrium unreachable in any reasonable time scale. It means the system by itself keeps some memory of its original quantum state. This property can be extremely useful for quantum computation, which cannot be implemented without connection between the remote parts of the Hilbert space, i.e. states localized in the computational basis are useless. The ergodic states should also be avoided: in the Hilbert space of high dimension they easily lose the quantum information. We will discuss evidences for the existence of delocalized non-ergodic systems and speculate about their properties by comparing them with non-integrable classical dynamical systems such as Solar Systems. Speaker Info: Boris Altshuler works in the field of Condensed Matter theory. He made substantial contributions to the understanding of the effects of disorder, quantum interference and interactions between electrons on the properties of bulk, low-dimensional, and mesoscopic conductors. Boris was educated in Russia. He graduated from the Leningrad (now St. Petersburg) State University and joined Leningrad Institute for Nuclear Physics first as a graduate student and later as a member of the research stuff. His PhD thesis advisor was Arkadii Aronov. After moving to USA Boris was on faculty of the Massachusetts Institute of Technology and later of the Princeton University. He was also a Fellow of NEC laboratories America (Princeton, NJ). Now he is a professor of Physics at Columbia University. Boris Altshuler is a recipient of a number of scientific awards - the most significant are 1993 Hewlett-Packard Europhysics Prize (Agilent Prize) and 2003 Oliver Buckley Prize of American Physical Society. He is a member of the National Academy of Sciences and of the American Academy of Arts and Sciences. He is also a foreign member of The Norwegian Academy of Science and Letters and of the Academy of Romanian Scientists.