Quantum annealing with antiferromagnetic transverse interactions for the Hopfield model

Quantum annealing with antiferromagnetic fluctuations.

We introduce antiferromagnetic quantum fluctuations into quantum annealing in addition to the conventional transverse-field term. We apply this method to the infinite-range ferromagnetic p-spin model, for which the conventional quantum annealing has been shown to have difficulties in finding the ground state efficiently due to a first-order transition. We study the phase diagram of this system ...

Quantum annealing in the transverse Ising model

We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between states and thus play the same role as thermal fluctuations in the conventional approach. The idea is tested by the transverse Ising model, in which the transverse field is a function of time similar to ...

Quantum annealing of the random-field Ising model by transverse ferromagnetic interactions.

We introduce transverse ferromagnetic interactions, in addition to a simple transverse field, to accelerate the convergence of quantum annealing of the random-field Ising model. The conventional approach using only the transverse-field term is known to be plagued by slow convergence when the true ground state has strong ferromagnetic characteristics for the random-field Ising model. The transve...

Quantum Hopfield Model

The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the α (the ratio of the number of stored patterns to the system size)-∆ (the strength of the transverse field) phase diagram of this model in the ground state resembles the α...

Quantum phase transitions in the transverse one-dimensional Ising model with four-spin interactions