Ion Trap Quantum Computers Part 1: 1-Qubit Gates

Abstract

Ions offer a promising approach to physically realize qubits. The present text extensively elucidates the physics of 1-qubit gates for use in quantum computers based on ion qubits. To keep the discussion as simple as possible, ions are treated mechanically as rigid rotors. The discussed system is excellently suited to practice important elementary methods of quantum physics using a practical application example. For didactic reasons, contrary to the usual approach, a typographical distinction is made between states and operators on the one hand and column vectors and matrices on the other. The article is aimed at readers with basic knowledge of quantum physics, i.e., those familiar with terms like Schrödinger equation, wave function, bra and ket, Pauli matrices, and the like. Rudimentary knowledge of quantum computers is also assumed (qubit, gate, ...).