Quantum annealing via transverse interaction with XY-type anisotropy

優也 関, Yuya Seki, 秀稔 西森 +1 more

Yôhei Saika, Tetsuya Kakimoto, Jun Ichi Inoue

We investigated quantum annealing (QA) via the transverse interaction with XY-type anisotropy for a ground state problem for a small composed of 4 S=1/2 quantum spins interacting with anti-ferromagnetic interactions with each other. By solving the Schrodinger equation for the QA system, we found that a preferable solution can be derived by tuning the XY-type anisotropy of the kinetic term among multiple candidates of the QA system. Similar behavior was suggested from the static property obtained by the spin wave theory established in statistical physics. In addition, we clarified that the ground state of the target system can be obtained by the QA starting from an initial state including excited states of the kinetic term, if the interval of time of the QA is set to be large to some extent.

Óscar Promio Muñoz

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.

秀稔 西森, Hidetoshi Nishimori, 隼一 井上 +1 more

正 鈴木, Sei Suzuki, 秀稔 西森 +2 more