The idea of state transfer is to develop schemes that allow the transfer of an unknown quantum state from one location to another. Such protocols might be very useful in the realisation of a practical quantum computer because many physical interactions between qubits are short range, and therefore only act on nearest-neighbours. To interact distant qubits, they must first be moved next to each other.
The simplest state transfer protocol that one can consider is a series of SWAP operations between pairs of nearest-neighbour qubits. However, this requires a significant degree of control and, hence, it is desireable to try and find other schemes which may be less complex and therefore less prone to errors.
A number of schemes have now been developed that require a single, time-independent, Hamiltonian to be applied between a series of qubits quant-ph/0309131,quant-ph/0411020,quant-ph/0501007,quant-ph/0408152. One particular example, from quant-ph/0309131, involves a Hamiltonian of the form
H=\frac{1}{4}\sum_{n=1}^{N-1}\sqrt{n(N-n)}\left(\sigma_x^n\sigma_x^{n+1}+\sigma_y^n\sigma_y^{n+1}\right)
which is particularly simple because it commutes with the total spin operator,
\sum_{n=1}^N\sigma_z^n
so we only have to examine what happens with an N × N matrix instead of 2N × 2N. This particular Hamiltonian is even simpler because it is just the same as the rotation matrix of a spin (N − 1)/2 particle.
Protocols have also been created that can accommodate errors in the Hamiltonian, at the cost of some additional interaction at either end of the transfer system quant-ph/0406112,quant-ph/0502186 and questions have also been addressed as to the capacity of such systems quant-ph/0312141.