Dynamical decoupling and NNN discrete quantum networks

Abstract

Perfect State Transfer is known to be possible on complex next-to-nearest-neighbor structures of qubits. The complexity of these networks coupled with the pervasive imperfections of the real world can lead to shortcomings in their practical construction. We analyze several realistic categories of flaws in the networks and show that they can have a harsh effect on the network’s performance. Dynamical decoupling is a known quantum error correction algorithm that can be used for partial or complete mitigation of undesired artefacts in quantum systems. We show here that dynamical decoupling can, in principle, also be used to stabilize the complex next-to-nearest-neighbor networks of qubits. We compare the proposed dynamical decoupling schemes with a baseline of dynamical decoupling scheme that eliminates all but one path to quantum state transfer on the network, thus effectively transforming it to a nearest-neighbor chain.

Quantum walk state transfer on a hypercube

“…If we have control over all sites we can globally design the dynamics such that the walker is transferred between a selected pair of vertices at a certain time. For the continuous time evolution, where the dynamics is governed by the Schroedinger equation with a given hamiltonian, the problem was investigated to large detail in the context of spin chains [5][6][7][8][9][10], discrete quantum networks of various topologies [11][12][13][14][15] and continuous time quantum walks [16][17][18][19][20]. In the discrete time case this approach was studied on various graphs such as circle [21,22], regular graphs [23] or more general networks [24].…”