Quaternionic description of semiconductor position-based qubits

TL;DR

This paper introduces a quaternionic framework for describing semiconductor single-electron qubits, providing a new mathematical approach to model their quantum evolution, especially in interacting multi-qubit systems.

Contribution

It formulates a conversion scheme from complex Hamiltonians to quaternionic form for single and multiple semiconductor qubits, enabling novel analysis of their quantum dynamics.

Findings

Quaternionic representation of quantum evolution operators.

Conversion scheme for Hamiltonians into quaternionic form.

Application to single and interacting multi-qubit systems.

Abstract

The quaternionic description of semiconductor single-electron devices is given in the single-electron regime. The conversion scheme of complex value Hamiltonian into a quaternion is formulated for the case of single-electron semiconductor qubit and many electrostatically interacting qubits. In particular, the quantum evolution operator is presented in quaternion form for the case of one and many electrostatically interacting quantum bodies.