Quaternionic description of semiconductor position-based qubits

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.