Computing spin networks

James Moffat

Louis Hirsch Kauffman, Samuel J. Lomonaco

Jakub Mielczarek A B

The article is addressing a possibility of implementation of spin network states on adiabatic quantum computer. The discussion is focused on application of currently available technologies and analyzes a concrete example of D-Wave machine. A class of simple spin network states which can be implemented on the Chimera graph architecture of the D-Wave quantum processor is introduced. However, extension beyond the currently available quantum processor topologies is required to simulate more sophisticated spin network states, which may inspire development of new generations of adiabatic quantum computers. A possibility of simulating Loop Quantum Gravity is discussed and a method of solving a graph non-changing scalar (Hamiltonian) constraint with the use of adiabatic quantum computations is proposed.

Francesca Albertini, Domenico D’Alessandro

Yuuki Nakamiya, Mitsunaga Kinjo, Osamu Takahashi +2 more

It has been known that a variety of optimization problems can be solved with a neural network, and that a quantum computer executes real parallel computation. A quantum neural network has been proposed to incorporate quantum dynamics into a neural network. In this study, we test the possibility of actual implementation of a quantum neural network with a nuclear spin as a qubit. First, we introduce the relationship between a spin and a neuron, then describe the adiabatic Hamiltonian evolution applied for the state change. Next, we describe a real spin quantum system and show the simulation results. A proposed nuclear spin system behaves as a neuron with inhibitory interactions, as expected in analogy to a Hopfield network.