Implementation of quantum gates based on geometric phases accumulated in the eigenstates of periodic invariant operators

Abstract

We propose a new strategy to physically implement a universal set of quantum gates based on geometric phases accumulated in the nondegenerate eigenstates of a designated invariant operator in a periodic physical system. The system is driven to evolve in such a way that the dynamical phase shifts of the invariant operator eigenstates are the same (or {\it mod} $2\pi$) while the corresponding geometric phases are nontrivial. We illustrate how this strategy to work in a simple but typical NMR-type qubit system.

4 pages

References in corpus (6)

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Cited by in corpus (6)

• Geometric vs. Dynamical Gates in Quantum Computing Implementations Using Zeeman and Heisenberg Hamiltonians
• Transitionless quantum driving in spin echo
• Decoherence of quantum gates based on Aharonov-Anandan phases in a multistep scheme
• Effect of decoherence on the Berry phase of a spin-half in a rotating magnetic field
• Robust composite two-qubit gates for silicon-based spin qubits
• Geometric and holonomic quantum computation