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Physical Review A

Scalable ion trap quantum computation in decoherence-free subspaces with pairwise interactions only

Kenneth R. Brown, Jiří Vala, K. Birgitta Whaley

Published Jan 17, 2003• 23 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.67.012309

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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.
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.
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.
We review recent experiments on entanglement, Bell's inequality, and decoherence-free subspaces in a quantum register of trapped \be ions. We have demonstrated entanglement of up to four ions using the technique of Mølmer and Sørensen. This method produces the state |down down> + |up up> for two ions and the state |down down down down> + |up up up up> for four ions. We generate the entanglement deterministically in each shot of the experiment. Measurements on the two-ion entangled state violates Bell's inequality at the 8σ8σ8σ level. Because of the high detector efficiency of our apparatus, this experiment closes the detector loophole for Bell's inequality measurements for the first time. This measurement is also the first violation of Bell's inequality by massive particles that does not implicitly assume results from quantum mechanics. Finally, we have demonstrated reversible encoding of an arbitrary qubit, originally contained in one ion, into a decoherence-free subspace (DFS) of two ions. The DFS-encoded qubit resists applied collective dephasing noise and retains coherence under ambient conditions 3.6 times longer than does an unencoded qubit. The encoding method, which uses single-ion gates and the two-ion entangling gate, demonstrates all the elements required for two-qubit universal quantum logic.