Physical systems for quantum computing

Nowadays, there exist many physical realizations of qubits for quantum computing. Some modern and prominent examples of types of quantum computer platforms are the superconducting qubits, spin qubits, trapped-ion qubits, photonic qubits and topological qubits. In this document, we overview the underlying physical principles of three of these platforms: superconducting qubits, spin qubits in semiconductors and trapped-ion qubits. This work is also meant to serve as an introduction to these technologies. This document is organized as follows. First, we introduce the so called DiVincenzo criteria [3] that de ne the requirements that a system has to meet to be useful as a quantum computer, with a brief explanation of the decoherence and the Bloch sphere. Second, we go through the three quantum computer platforms. The second part begins with an introduction to the superconducting qubits by explaining some basic concepts of superconductivity such as the Meissner effect and the flux quantization on a superconducting ring. This is done in order to understand the basics of the Josephson junctions used in this type of qubits. Then, the three main types of superconducting qubits are explained. Superconducting qubits can be divided on three main types depending on the variable chosen to encode the qubit state: charge qubits, phase qubits and flux qubits. In the sections dedicated to the charge qubits, the Cooper pair box, which is the predecessor to the transmon qubit, is explained in order to understand the transmon qubits. We focus our attention mainly on the transmon qubit because it seems to be the most popular type of superconducting qubit. In the following sections, the spin qubits and the trapped-ion qubits are also explained. There are also different possibilities for implementing spin qubits like, for example, in NV-centers in a diamond lattice, color centers, spins on molecules, shallow dopants or electrostatically confined quantum dots in semiconductors. We focus on the latter. For trapped-ion qubits there are different state encoding possibilities depending on the energy levels used as computational subspace so, for example, we have Zeeman, hyperfine, optical and fine-structure trapped-ion qubits. Each section corresponding to the different qubit implementations explained on this work follows the same basic scheme. The explanation of each implementation is done by showing how it satisfies the five DiVincenzo criteria.