Quaternions and the Quantum

Ulli Wolff A

Songsong Dai

Quaternionic quantum theory is a generalization of the standard complex quantum theory. Inspired by this, we study the quaternionic quantum computation using quaternions. We first develop a theory of quaternionic quantum automata as a model of quaternionic quantum computation. Quaternionic quantum automata also can be seen as an extension of complex quantum automata. Then we introduce some operations of quaternionic quantum automata and establish some of their basic properties.

Lawrence Paul Horwitz, Lawrence C. Biedenharn, Daniel Sepunaru

Songsong Dai

Quaternionic quantum theory is an extension of the standard complex quantum theory. Inspired by this, we study the quaternionic quantum computation using quaternions. We first develop a theory of quaternionic quantum Turing machines as a model of quaternionic quantum computation. Quaternionic quantum Turing machines can also be seen as a generalization of the complex quantum Turing machine. Then, we introduce the weighted sum of quaternionic quantum Turing machines and establish some of their basic properties.

W. S. Anglin, Jim Lambek

Eduardo Jose Bayro-Corrochano, Samuel Solis-Gamboa

Since the introduction of quaternion by Hamilton in 1843, quaternions have been used in a lot of applications. One of the most interesting qualities is that we can use quaternions to carry out rotations and operate on other quaternions; this characteristic of the quaternions inspired us to investigate how the quantum states and quantum operator work in the field of quaternions and how we can use it to construct a quantum neural network. This new type of quantum neural network (QNN) is developed in the quaternion algebra framework that is isomorphic to the rotor algebra [Formula: see text] of the geometric algebra and is based on the so-called qubit neuron model. The quaternion quantum neural network (QQNN) is tested and shows robust performance.