08w5103 Quantum Computation with Topological Phases of Matter

Arriving Sunday, July 20 and departing Friday, July 25, 2008

Organizers: Marcel Franz (University of British Columbia), Michael H. Freedman (Microsoft Corporation), Yong-Baek Kim (University of Toronto), Chetan Nayak (University of Calilfornia, Los Angeles), Kirill Shtengel (University of Calilfornia Riverside).

Confirmed Participants

Press Release: Quantum Computation with Topological Phases of Matter

Information for Participants

Schedule (PDF file)

Mailing List

Final Report (PDF file)

Objectives

Although the idea of topological quantum computation as a mathematical concept is now well-established [Kitaev (1997); Freedman (2001); Freedman, Kitaev, Larsen and Wang (2001); Freedman, Larsen and Wang (2002)], relatively little work has gone into its physical realization. In fact, very few basic principles underlying topological quantum computation using anyons have been worked out, and the existence of suitable condensed matter systems (e.g. quantum Hall systems, quantum magnets, quantum dot and Josephson junction arrays) is still in doubt. In addition, currently there are no firmly established practical schemes for carrying out the final state read-out in a topological quantum computer (even if a suitable system, e.g. some exotic fractional quantized Hall state, can be identified). On the other hand, the conceptual proposal of fault-tolerant topological quantum computation has had a large impact because of the deep connections it establishes between topology, condensed matter physics, and quantum computation.

The goal of this workshop is to both study the physical nature of topological phases as well as to address the most important theoretical issues connected with any attempt to practically realize a topological quantum computer. One of the main objectives of the proposed workshop is to bring together experts from different fields including condensed matter physics, quantum optics, mathematics, and quantum information. The exchange of ideas between researchers working on these subjects will hopefully result in making new inroads into this broad, inter-disciplinary field. Specifically, we hope to focus on the following topics.

1. Physical systems with topological order. So far, of experimentally observed systems, only Fractional Quantum Hall systems are believed to possess topological order. Numerous other possibilities have been discussed recently, including atomic systems in optical lattices, Josephson junction arrays, frustrated magnetic systems and unconventional superconductors. How to engineer systems supporting a topological phase remains an open question. No one has yet provided clear experimental evidence of any exotic statistics in any system. Experimental detection of topological order, or even detection of its slightly less exotic cousin -- fractional statistics -- remains an open problem. How to control topological excitations, a crucial part of building a topological quantum computer, also remains to be explored.

2. Model Hamiltonians and mathematical structures. Recently, advances have been made towards understanding which specific types of materials and/or Hamiltonians could support a topological phase. Yet, much remains unknown. Most disturbingly, a general scheme for classifying topological orders (akin to the Landau theory of symmetry breaking for conventional orders) is lacking. Part of the workshop proposed here is concerned with understanding which model Hamiltonians might have topological phases, how to classify these in full generality, and which could support universal quantum computation.

3. Topological Algorithms and Computational Architectures. Given that such topological phases do exist, and are capable of performing universal quantum computation, one must ask how to build efficient architecture and how one would actually go about performing such computations. The structure of topological phases is extremely complex and imposing the traditional qubit architecture may not be the most efficient scheme.