## 3 Research Objectives, Materials and Methods
### Typical Contents Considered in the Different Educative Elements
\begin{table}
\begin{tabular}{l c c} \hline \hline  & **Theoretical Contents Developed in the Formal Courses (Research Stay and Minor)** & **Integration** \\
**Unit Name** & **Topics Description** & **Integration** \\ \hline Introduction & * Brief history of quantum mechanics and notable experiments & 3 \\  & * Stern–Gerlach experiment and physical conjugate variables & 1, 3 \\ Dirac notation & * quantum states, kets, Hilbert spaces, dual space, bras, and inner product & 1, 2 \\ and basic definitions & * State decays, associated probabilities and quantum fidelity & 1 \\  & * Outer product and operators: Dirac and matrix representations & 1 \\  & * Unitary, Hermitian, Normal, and Projective operators & 1 \\  & * Projective and weak measurements, measurement operators and probabilities & 1, 2 \\  & - Operator functions, Schrödinger equation and evolution operator & 1 \\  & * Qubits, Bloch representation and the \(SU(2)\) group & 1, 2 \\  & * Pauli operators, commutators, anti-commutators, and properties & 1 \\ Composed systems & * Tensor products, states and operators of composed systems & 1 \\  & * Entanglement, Schmidt coefficients, Bell states, and entanglement measures & 1 \\  & - Quantum mechanics in postulates & - \\ Quantum circuits & * quantum states evolution as a circuit & 1, 2 \\  & * Not, CNOT, Hadamard, controlled and other gates & 1, 2 \\  & * Direct and inverse Bell circuits & 1, 2 \\  & * Teleportation algorithm for single and composed qubits & 1, 2 \\  & * BB84 protocol & 3 \\  & - Deutsch–Josza problem & 1 \\  & - Grover algorithm & 1, 2 \\ Mixed states & - Quantum Fourier transform & 1 \\  & - Pure and mixed states concept, physical interpretation of a mixture & 1 \\  & - Density operator and matrix, populations and coherences & 1 \\  & - Trace, partial trace, and partial transpose & 1 \\  & - Definitions for mixed states: probability, measurement, expected values, and evolution & 1 \\  & - Bloch ball and Bloch representation of mixed states & 1 \\ Quantum communication & - Quantum channels, Kraus operators and Pauli channels & 1 \\  & - Syndromes and quantum error correction & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Central contents for quantum information course included in the research stay and minor with the computer simulations and experiments included in QUANTUM (1), QISKIT (2), and Photonics experiments and demonstrations (3). \begin{table}
\begin{tabular}{l l l} \hline \hline  & **Contents of Computer-Based Applications And Experimental Innovations Sections** & **(3) Photonics E\&D/Optics Studio** \\
**(1) QUANTUM** & **(2) QISKIT** & **Polarization and Stern–Gerlach effects** \\ \hline States, operators and measurements & Quantum and classical registers & Polarization and Stern–Gerlach effects \\ Bell circuit (direct and inverse) & States initialization with operations & Quartz polarization beam splitters \\ Qubit rotations and measurements & Defining composed gates & Interferometers arrangements and mirrors \\ Teleportation circuit & Bell, Teleportation and Grover circuits & Polarization rotators \\ Deutsch-Jozsa algorithm & Quantum simulations and Ising model & Bomb tester experiment \\ Grover algorithm & Adiabatic quantum computation & Quantum eraser experiment \\ Quantum Fourier Transform & Protein folding and chemical potentials & BB84 cryptography protocol \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Practices commonly developed using the computer-based applications (QUANTUM, QISKIT) and photonics experiments included in the courses (Research stay and Minor). Full-Blended Learning Approach during the COVID-19 Lockdown: An Effective Approach Attaining Planned Research and Educative Goals  
All the previous initiatives reported were implemented over time (see Figure 4), improving and adapting the contents to the research projects to involve the students. They all were stated to support research culture [50]. Figure 4 shows them from 2010 to 2022.