Holonomic quantum computation

✍ Scribed by Paolo Zanardi; Mario Rasetti

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 77 KB
• Volume: 264
• Category: Article
• ISSN: 0375-9601
• DOI: 10.1016/s0375-9601(99)00803-8

✦ Synopsis

We show that the notion of generalized Berry phase i.e., non-abelian holonomy, can be used for enabling quantum computation. The computational space is realized by a n-fold degenerate eigenspace of a family of Hamiltonians parametrized by a manifold M M. The point of M M represents classical configuration of control fields and, for multi-partite systems, couplings between subsystem. Adiabatic loops in the control M M induce non trivial unitary transformations on the computational space. For a generic system it is shown that this mechanism allows for universal quantum computation by composing a generic pair of loops in M M.