Non-adiabatic transitions in nonlinear quantum systems

We propose a general description of adiabatic evolution of degenerate quantum systems in both linear and nonlinear cases. We derive the effective evolution equations of the considered system. For nondegenerate cases, we obtain a generalized Berry's phase for nonlinear systems. For linear cases, the equations reduce to the Wilczek-Zee dynamics in degenerate quantum systems, where non-Abelian adiabatic connections appear. The method can be used to study the coherent atom-molecule transition in ultracold quantum gases with degeneracy and is consistent with quantized treatment.We propose a general description of adiabatic evolution of degenerate quantum systems in both linear and nonlinear cases. We derive the effective evolution equations of the considered system. For nondegenerate cases, we obtain a generalized Berry's phase for nonlinear systems. For linear cases, the equations reduce to the Wilczek-Zee dynamics in degenerate quantum systems, where non-Abelian adiabatic connections appear. The method can be used to study the coherent atom-molecule transition in ultracold quantum gases with degeneracy and is consistent with quantized treatment.

Physical Review AApr 15, 20105 citations

Nonlinear Adiabatic Evolution of Quantum Systems

Jie Liu, Sheng-Chang Li, Libin Fu +1 more

Springer eBooksJan 1, 201811 citations

Quantum annealing with symmetric subspaces

Takashi Imoto, Yuya Seki, Yuichiro Matsuzaki

Quantum annealing (QA) is a promising approach for not only solving combinatorial optimization problems but also simulating quantum many-body systems such as those in condensed matter physics. However, non-adiabatic transitions constitute a key challenge in QA. The choice of the drive Hamiltonian is known to affect the performance of QA because of the possible suppression of non-adiabatic transitions. Here, we propose the use of a drive Hamiltonian that preserves the symmetry of the problem Hamiltonian for more efficient QA. Owing to our choice of the drive Hamiltonian, the solution is searched in an appropriate symmetric subspace during QA. As non-adiabatic transitions occur only inside the specific subspace, our approach can potentially suppress unwanted non-adiabatic transitions. To evaluate the performance of our scheme, we employ the XY model as the drive Hamiltonian in order to find the ground state of problem Hamiltonians that commute with the total magnetization along the $z$ axis. We find that our scheme outperforms the conventional scheme in terms of the fidelity between the target ground state and the states after QA.Quantum annealing (QA) is a promising approach for not only solving combinatorial optimization problems but also simulating quantum many-body systems such as those in condensed matter physics. However, non-adiabatic transitions constitute a key challenge in QA. The choice of the drive Hamiltonian is known to affect the performance of QA because of the possible suppression of non-adiabatic transitions. Here, we propose the use of a drive Hamiltonian that preserves the symmetry of the problem Hamiltonian for more efficient QA. Owing to our choice of the drive Hamiltonian, the solution is searched in an appropriate symmetric subspace during QA. As non-adiabatic transitions occur only inside the specific subspace, our approach can potentially suppress unwanted non-adiabatic transitions. To evaluate the performance of our scheme, we employ the XY model as the drive Hamiltonian in order to find the ground state of problem Hamiltonians that commute with the total magnetization along the $z$ axis. We find that our scheme outperforms the conventional scheme in terms of the fidelity between the target ground state and the states after QA.

arXiv:2209.09575Sep 20, 20220 citations

z

axis. We find that our scheme outperforms the conventional scheme in terms of the fidelity between the target ground state and the states after QA.