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arXiv:quant-ph/0407212 · Physical Review A

Perfect state transfer, effective gates, and entanglement generation in engineered bosonic and fermionic networks

Man‐Hong Yung, Sougato Bose

Published Mar 14, 2005• 191 citations
arXivHTMLPDF

Abstract

We show how to achieve perfect quantum state transfer and construct effective two-qubit gates between distant sites in engineered bosonic and fermionic networks. The Hamiltonian for the system can be determined by choosing an eigenvalue spectrum satisfying a certain condition, which is shown to be both sufficient and necessary in mirror-symmetrical networks. The natures of the effective two-qubit gates depend on the exchange symmetry for fermions and bosons. For fermionic networks, the gates are entangling (and thus universal for quantum computation). For bosonic networks, though the gates are not entangling, they allow two-way simultaneous communications. Protocols of entanglement generation in both bosonic and fermionic engineered networks are discussed.

DOI
10.1103/physreva.71.032310

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We show how to achieve perfect quantum state transfer and construct effective two-qubit gates between distant sites in engineered bosonic and fermionic networks. The Hamiltonian for the system can be determined by choosing an eigenvalue spectrum satisfying a certain condition, which is shown to be both sufficient and necessary in mirror-symmetrical networks. The natures of the effective two-qubit gates depend on the exchange symmetry for fermions and bosons. For fermionic networks, the gates are entangling (and thus universal for quantum computation). For bosonic networks, though the gates are not entangling, they allow two-way simultaneous communications. Protocols of entanglement generation in both bosonic and fermionic engineered networks are discussed.
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We find analytic models that can perfectly transfer, without state initialization or remote collaboration, arbitrary functions in two- and three-dimensional interacting bosonic and fermionic networks. This provides for the possible experimental implementation of state transfer through bosonic or fermionic atoms trapped in optical lattices. A significant finding is that the state of a spin qubit can be perfectly transferred through a fermionic system. Families of Hamiltonians are described that are related to the linear models and that enable the perfect transfer of arbitrary functions. Furthermore, we propose methods for eliminating certain types of errors.
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