Nonlinear Phenomena in Complex Systems, 2010, Vol.13, No.1, pp.1-12

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2010, Vol.13, No.1, pp.1-12

Stability of Holonomic Quantum Computations with Respect to Control Errors.
Viatcheslav I. Kuvshinov and Andrei V. Kuzmin

We give a brief review based mainly on our own research in the field of stability of holonomic quantum computers (HQC) with respect to random errors in assignment of control parameters. We discuss the internal robustness typical to HQC and ways to improve it in some specific implementations. Connection with the work done in the field by another authors is analyzed as well. Derived simple linear formulae connecting the Hadamard gate fidelity and the purity of the final state for a wide class of HQC is discussed and generalized in the context of quantum channels depending on a number of classical control parameters. The results are checked on a number of particular examples, namely, one-qubit quantum gates both holonomic and dynamical implemented in the framework of the ion trap setup and the single qubit anisotropic depolarizing quantum channel.
Key words: holonomic quantum computer, Hadamard gate fidelity, control

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