Abstract:
We consider a communication line formed by spin-1/2 particles and consisting of a transmitter, a receiver, and a transmission line connecting them. Furthermore, the receiver, together with several neighboring spins, forms a so-called extended receiver, to which a unitary transformation is applied, ensuring the necessary condition for ideal transfer. The evolution of the system is governed by an XX Hamiltonian that preserves the number of spin excitations. The problem consists of transferring the initial pure state of the transmitter to the receiver, with all spins of the transmission line and receiver initially in the ground state. At some point after the onset of evolution, a unitary transformation is applied to the extended receiver. This transformation is designed such that terms in which all excitations are concentrated on the spins of the receiver are extracted from the entire superposition state of the system, with the pure state of the receiver being proportional to the initial pure state of the transmitter. Maximizing this proportionality coefficient in absolute value is an optimization problem for the parameters of the specified unitary transformation, which is solved analytically within the framework of the algorithm under consideration. The remaining terms of the superposition state are of no interest. To eliminate them, a single-qubit ancilla is introduced, whose excited state (state 1) is associated with the above-mentioned informative part of the superposition state. If we now measure the ancilla's state with the desired result of 1, the receiver's state at the time of measurement will match the transmitter's initial state, thereby completing the perfect transfer algorithm. For the algorithm to operate effectively, the probability of obtaining the desired measurement result can be significantly less than one and estimated at $\sim 0.5$. This means that to register perfect transfer with this probability, the algorithm must be repeated $\sim 3$ times.
This work was funded by FRC PCP MC RAS under state assignment number 124013000760-0.
