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

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.

Figure 1

In engineered fermionic and bosonic chains, when the spectrum of the single-particle Hamiltonian in Eq. (3) satisfies the relation (12), effective gates on mirror-conjugate pairs of sites, such as $(x,\overline{x})$ and $(y,\overline{y})$, can be constructed by free network evolution.