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Non-Abelian Berry connections for quantum computation

Jiannis Pachos·Paolo Zanardi·Mario Rasetti
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Abstract

In the holonomic approach to quantum computation information is encoded in a degenerate eigenspace of a parametric family of Hamiltonians and manipulated by the associated holonomic gates. These are realized in terms of the non-abelian Berry connection and are obtained by driving the control parameters along adiabatic loops. We show how it is possible, for a specific model, to explicitly determine the loops generating any desired logical gate, thus producing a universal set of unitary transformations. In a multi-partite system unitary transformations can be implemented efficiently by sequences of local holonomic gates. Moreover a conceptual scheme for obtaining the required Hamiltonian family, based on frequently repeated pulses, is discussed, together with a possible process whereby the initial state can be prepared and the final one can be measured.

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Jiannis Pachos, Paolo Zanardi, Mario Rasetti. 1999-11-11. Non-Abelian Berry connections for quantum computation. https://doi.org/10.1103/physreva.61.010305

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