Noisy Control, the Adiabatic Geometric Phase, and Destruction of the Efficiency of Geometric Quantum Computation

Details Noisy Control, the Adiabatic Geometric Phase, and Destruction of the Efficiency of Geometric Quantum Computation Noisy Control, the Adiabatic Geometric Phase, and Destruction of the Efficiency of Geometric Quantum Computation

2003-11-30

arxiv.org/abs/quant-ph/0312008v1

Physics

Quantum Physics

4 pages, no figures, submitted to Phys. Rev. Lett

Scientific paper

We examine the adiabatic dynamics of a quantum system coupled to a noisy classical control field. A stochastic phase shift is shown to arise in the off-diagonal elements of the system's density matrix which can cause decoherence. We derive the condition for onset of decoherence, and identify the noise properties that drive decoherence. We show how this decoherence mechansim causes: (1) a dephasing of the observable consequences of the adiabatic geometric phase; and (2) the loss of computational efficiency of the Shor algorithm when run on a sufficiently noisy geometric quantum computer.

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