A review of perfect quantum state transfer, from one to two and three dimensional arrays of qubits

Abstract

In the light of recent advances in fabricating single layer quantum chips and a possible road toward development of multi-layer quantum chips, we review, in a detailed way, the subject of quantum state transfer with particular emphasis on perfect quantum state transfer in two and three dimensional lattices. We show how one can route an unknown quantum state from one node in a single layer of a quantum chip to another one on another layer with unit fidelity. Our method of presentation in this review allows the reader with a modest background in quantum mechanics to grasp the essential ideas and methods of this important branch of quantum information theory.

Figures (10)

• Figure 1: The quasi-one dimensional chain with uniform couplings for perfect transfer of quantum states.
• Figure 2: The double chain setup for conclusive state transfer of Burgarth1Burgarth2. The first two qubits are controlled by Alice (A) and the last two ones by Bob (B).The protogol is robust if the couplings show small variations, i.e. of the form $J_i=J(1+\delta_i)$ and $J'_i=J(1+\delta'_i)$ for small $\delta_i$ and $\delta'_i.$.
• Figure 3: The pattern of couplings in a short chain. The barchart below shows the couplings for a chain of length 20.
• Figure 4: With the identification (\ref{['nn']}) the evolution operator $U$ perfectly transfers an excitation from the left hand side of the chain to the right hand side.
• Figure 5: The quasi-one dimensional chain with uniform couplings for perfect transfer of quantum states. The figure below shows that the chain can be decomposed as a sequence of short chains of length 2 and 3.