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Holonomic Quantum Computation

Paolo Zanardi·Mario Rasetti
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Abstract

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 $\cal M$. The point of $\cal M$ represents classical configuration of control fields and, for multi-partite systems, couplings between subsystem. Adiabatic loops in the control $\cal M$ 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 $\cal M.$

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Paolo Zanardi, Mario Rasetti. 1999-11-15. Holonomic Quantum Computation. https://doi.org/10.1016/s0375-9601(99)00803-8

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