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arXiv:quant-ph/0603222 · Physical Review A

Scalable quantum computation in decoherence-free subspaces with trapped ions

Li-Xiang Cen, Z. D. Wang, Shun-Jin Wang

Published Sep 19, 2006• 36 citations
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Abstract

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.

DOI
10.1103/physreva.74.032321

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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.
We show that universal ion trap computation can be performed on decoherence-free subspaces (DFS's) using only two-qubit operations. One logical qubit is minimally encoded into three physical qubits. The encoded qubit is in a DFS under collective decoherence. Encoded single- and two-qubit logical operations are implemented via the S\o{}rensen-M\o{}lmer interaction. We show that alternation of the effective Hamiltonians for two particular phase configurations of control fields approximates an anisotropic exchange interaction that has recently been shown to be universal on these encodings. Physically realistic rapid alternation of the control fields also approximates evolution in a DFS. Our scheme is scalable in a recently proposed array-based architecture.
Universal ion trap computation on Decoherence Free Subspaces (DFS) using only two qubit operations is presented. The DFS is constructed for the collective dephasing model. Encoded single and two-qubit logical operations are implemented via the Sorensen-Molmer interaction. Alternation of the effective Hamiltonians for two particular phase configurations of control fields approximates an anisotropic exchange interaction. This is universal over suitable encodings of one logical qubit into three physical qubits which are also DFS under collective decoherence.
Any residual coupling of a quantum computer to the environment results in computational errors. Encoding quantum information in a so-called decoherence-free subspace provides means to avoid these errors. Despite tremendous progress in employing this technique to extend memory storage times by orders of magnitude, computation within such subspaces has been scarce. Here, we demonstrate the realization of a universal set of quantum gates acting on decoherence-free ion qubits. We combine these gates to realize the first controlled-NOT gate towards a decoherence-free, scalable quantum computer.
A general scheme to perform universal, fault-tolerant quantum computation within decoherence-free subspaces (DFSs) is presented. At most two-qubit interactions are required, and the system remains within the DFS throughout the entire implementation of a quantum gate. We show explicitly how to perform universal computation on clusters of the four-qubit DFS encoding one logical qubit each under spatially symmetric (collective) decoherence. Our results have immediate relevance to quantum computer implementations in which quantum logic is implemented through exchange interactions, such as the recently proposed spin-spin coupled quantum dot arrays and donor-atom arrays.