Interplay between anisotropic exchange coupling and the swap operation in the two-qubit Heisenberg XY model

Wen Yin, J.-Q. Liang, Q.W. Yan

Guo‐Feng Zhang, Yue Zhou

Pouyan Ghiasi, Somayyeh Ghorbani, Seyed Mohammad Hosseiny +3 more

Guo-Hui Yang, Xiang Yang Miao, Jun Feng Zhang

A. Ege, Özgür Esat Müstecaplıoğlu

Graph structure of quantum spin networks plays an essential role in applying quantum annealing (QA). The Ising model is the typical choice to describe the interactions between the spins in the networks. Here, we explore the interplay of different interaction types between the spins and the structure of the underlying network on the performance of QA. Specifically, we consider the Heisenberg XY and antisymmetric anisotropic exchange interaction models, in addition to the usual Ising Model, in graph structures ranging from linear chains to complete graphs with different connectivities. We find that the QA performance of the Ising model shows less variation with the change of graph structure among different interaction types. The Heisenberg XY model suffers from significant performance losses with increasing connections beyond linear chains, which we attribute to increasing entropy built-up. Anisotropic exchange interactions turn out to be an impractical choice for complete graphs due to the diminishing energy gap during annealing. Furthermore, we investigate the effect of inhomogeneous couplings and reveal a trade-off between coupling strength and performance, especially significant for the case of the anisotropic exchange model.

Guofeng Zhang

Mutual information and swap operation in the two-qubit Heisenberg model with the Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interaction are investigated. It is found that the mutual information I of such a quantum channel is sensitive to the initial conditions and declines with increase in temperature. The DM interaction can lead to higher mutual information, especially for the ferromagnetic case. The entanglement quality of input states cannot enhance the mutual information of the quantum channel. When the DM interaction is large, the mutual information will have the maximum value of 2 for a non-entangled input state, but it is 1 for a maximally entangled input state. It is also shown that the swap operation can be implemented for some kinds of DM coupling. The conditions of the DM coupling under which the swap operation is feasible are established.