Invitation to topological quantum computation

Topologyをどういう風に取り入れるのかと楽しみにしていた。
Topologyといっても、anyonのflipを紐の交差であらわしたり、∪を生成、∩を消滅としたり素朴な描象だった。

講師: Giacomo Marmorini（慶應義塾大学日吉物理学教室）
題目: 「Invitation to topological quantum computation」
日時: 2009 年 7月 14日（火） 午後 4 時 30 分 〜 午後 6 時
場所: 慶應義塾大学日吉キャンパス 第 2 校舎 2 階 221 番教室
概要:

The realization of the quantum computer is one of the greatest scientific challenges of the present day. Efforts in this direction involve both theoretical and experimental physicists, as well as computer scientists. The unit of quantum information, or qubit, can be thought of as a two-level quantum system. Operations on one or more qubits are then unitary transformations on quantum states. For its own nature a quantum computer is subject to two major sources of errors: interaction with the environment (that leads to quantum decoherence) and imprecision of unitary transformations. A recent and physically interesting trend aims to overcome the error problem　with a completely new approach, namely Topological Quantum Computation (TQC). TQC relies upon topological, not local, properties of the system, so as to preserve it from local perturbations to a very large extent. The key ingredients are particle-like objects with generalized statistics (anyons), which do exist in 2+1 dimensions, in a degenerate ground state, that can be adiabatically moved around one another. Their trajectories braid in spacetime, which amounts to a non-trivial unitary transformation due to generalised statistics under identical particle interchange.
Besides illustrating the fundamental ideas of TQC, we give a general description of some of the leading candidates for its physical implementation, such as FractionalQuantum Hall Effect and
p-wave superconductors.