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arXiv:quant-ph/0111086 · Science

Geometric Manipulation of Trapped Ions for Quantum Computation

L.-M. Duan, J. I. Cirac, P. Zoller

Published Jun 1, 2001• 793 citations
arXivHTMLPDF

Abstract

We propose an experimentally feasible scheme to achieve quantum computation based solely on geometric manipulations of a quantum system. The desired geometric operations are obtained by driving the quantum system to undergo appropriate adiabatic cyclic evolutions. Our implementation of the all-geometric quantum computation is based on laser manipulation of a set of trapped ions. An all-geometric approach, apart from its fundamental interest, offers a possible method for robust quantum computation.

DOI
10.1126/science.1058835

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We propose an experimentally feasible scheme to achieve quantum computation based solely on geometric manipulations of a quantum system. The desired geometric operations are obtained by driving the quantum system to undergo appropriate adiabatic cyclic evolutions. Our implementation of the all-geometric quantum computation is based on laser manipulation of a set of trapped ions. An all-geometric approach, apart from its fundamental interest, offers a possible method for robust quantum computation.
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Non-adiabatic holonomic quantum computation, which recently attained a considerable attention, offers a promising approach for implementation of fast, universal, and robust quantum information processing. In this all-geometric approach, quantum gates are all based on non-adiabatic extensions of the geometric Berry phase effects. Apart from its fundamental and conceptual aspects, physical realizations of proposed mathematical structures play central role in the development of large-scale quantum computation. Here, we propose an experimentally feasible nano-engineered solid-state structure to realize geometric quantum computation via non-adiabatic quantum holonomies. We use a system of three coupled quantum dots containing a single electron, where two states of a double quantum-dot charge qubit interact through an intermediate quantum dot. Careful control of the inter-dot tunneling parameters makes it possible to create a geometric model system, which allows for robust and efficient quantum information processing.
We propose a scheme for the realization of unconventional geometric two-qubit phase gates with two identical two-level ions. In the present scheme, the two ions are simultaneously illuminated by a standing-wave laser pulse with its pulse frequency being tuned to the ionic transition. The gate operation time can be much shorter, making the system robust against decoherence. In addition, we choose the appropriate experimental parameters to construct the geometric phase gate in one step, and thus avoid implementing the pure geometric single qubit operation.
We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time.
We propose a decoherence-free subspace (DFS) scheme to realize scalable quantum computation with trapped ions. The spin-dependent laser-ion coupling is exploited in the presence of Coulomb interactions. A universal set of unconventional geometric quantum gates is achieved in encoded subspaces that are immune from decoherence by collective dephasing. The scalability of the scheme for an ion-array system is demonstrated, either by adiabatically switching on and off the interactions, or by a fast gate scheme with DFS encoding and noise-decoupling techniques.