• ES Español
• EN English

5.60. Quantum Computing (Elective)

5.60.1. Justification ↑ Back to top

This course introduces the fundamental principles of quantum computing, including qubits, superposition, entanglement, quantum algorithms, and hardware. Students will contrast classical and quantum models, exploring applications in cryptography, optimization, physical simulation, and quantum machine learning, using frameworks like Qiskit or Cirq. Includes a practical module on hardware architectures (superconductors, ion traps) and their impact on algorithm design.

5.60.2. Generales Goals ↑ Back to top

1. Understand the postulates of quantum mechanics applied to computing.
2. Implement basic quantum circuits and optimization algorithms.
3. Analyze the ethical, technical, and commercial impact of quantum computing.
4. Evaluate hardware limitations in real-world applications.

5.60.3. Contribution to Outcomes ↑ Back to top

AG-C11) Use of Tools: Applies modern computing tools in problem solving. (Usage)

AG-C10) Inquiry: Studies complex computing problems using information science methods. (Usage)

5.60.4. Content ↑ Back to top

5.60.4.1. Foundational concepts (10 hours) [Skills AG-C10,AG-C11] ↑ Back to top

Bibliography: (Nielsen and Chuang, 2010; Team, 2023)

Topics

1. Qubits and Bloch sphere representation.
2. Postulates of quantum mechanics.
3. Quantum gates (Hadamard, CNOT, Toffoli).

Learning Outcomes

1. Mathematically model a qubit [Usage].
2. Simulate basic operations in Qiskit [Assessment].

5.60.4.2. Quantum Architectures (10 hours) [Skills AG-C10,AG-C11] ↑ Back to top

Bibliography: (Möttönen and Vartiainen, 2023; IBM Research, 2023)

Topics

1. Principles:
2. The wave-particle duality principle
3. The uncertainty principle in the double-slit experiment
4. What is a Qubit? Superposition, interference, and measurement. Photons as qubits
5. Systems of two qubits, Entanglement, Bell states, The No-Signaling theorem enumerate
6. Axioms of QM: superposition principle, measurement axiom, unitary evolution
7. Single qubit gates for the circuit model of quantum computation: X, Z, H
8. Two qubit gates and tensor products, working with matrices
9. The No-Cloning Theorem. The Quantum Teleportation protocol
10. Algorithms:
11. Simple quantum algorithms: Bernstein-Vazirani, Simon's algorithm
12. Implementing Deutsch-Josza with Mach-Zehnder Interferometers
13. Quantum factoring (Shor's Algorithm)
14. Quantum search (Grover's Algorithm) enumerate
15. Implementation aspects:
16. The physical implementation of qubits
17. Classical control of a Quantum Processing Unit (QPU)
18. Error mitigation and control, NISQ and beyond
19. Measurement approaches enumerate
20. Emerging Applications:
21. Post-quantum encryption
22. The Quantum Internet
23. Adiabatic quantum computation (AQC) and quantum annealing enumerate

Learning Outcomes

1. Discuss how a quantum object produced as a particle propagates like a wave and is detected as a particle with a probability distribution corresponding to the wave [Debate]
2. Discuss the quantum-level nature that is inherently probabilistic [Debate]
3. Express your view on entanglement that can be used to create non-classical correlations, but there is no way to use quantum entanglement to send messages faster than the speed of light [Evaluate]
4. Describe quantum parallelism and the role of constructive vs destructive interference in quantum algorithms given the probabilistic nature of measurement(s) [Describe]
5. Analyze a code snippet providing the role of quantum Fourier transform (QFT) in Shor's algorithm [Analyze]
6. Write a program to implement Shor's algorithm in a simulator, highlighting the classical components and aspects of Shor's algorithm [Write]
7. Enumerate the specifics of each qubit modality (e.g., trapped ion, superconducting, silicon spin, photonic, quantum dot, neutral atom, topological, color center, electron-on-helium) [Enumerate]
8. Contrast AQC with the gate model of quantum computation and the problems each is better suited to solve [Contrast]

5.60.4.3. Algorithmic Strategies (12 hours) [Skills AG-C10,AG-C11] ↑ Back to top

Bibliography: (Preskill, 2018; Team, 2023)

Topics

1. Quantum computing
2. Deutsch-Jozsa algorithm.
3. Grover's search (applied to combinatorial optimization).
4. Shor's factorization and its impact on RSA.

Learning Outcomes

1. Implement Grover for SAT problems [Usage].

5.60.4.4. Formal Languages and Automata (10 hours) [Skills AG-C10,AG-C11] ↑ Back to top

Bibliography: (Schuld and Petruccione, 2021; Bravyi et al., 2022)

Topics

1. Quantum computation:
2. Postulates of quantum mechanics:
3. State space
4. State evolution
5. State composition
6. State measurement enumerate
7. Column vector representations of qubits
8. Matrix representations of quantum operations
9. Simple quantum gates (e.g., XNOT, CNOT) enumerate
10. Quantum Approximate Optimization Algorithm (QAOA).
11. Logistics/finance applications (Portfolio Optimization).

Learning Outcomes

1. For a quantum system give examples that explain the following postulates:
2. State Space - system state represented as a unit vector in Hilbert space
3. State Evolution - the use of unitary operators to evolve system state
4. State Composition - the use of tensor product to compose systems states
5. State Measurement - the probabilistic output of measuring a system state. enumerate [Familiarity].
6. Design a QAOA for routing problems [Assessment].

5.60.4.5. Ethics and Post-Quantum Security (6 hours) [Skills AG-C10,AG-C11] ↑ Back to top

Bibliography: (Team, 2019)

Topics

1. Post-quantum cryptography (NIST PQC Standardization).
2. Quantum supremacy: technical/ethical debate.
3. Patents and quantum geopolitics.

Learning Outcomes

1. Propose post-quantum migration strategies [Familiarity].

5.60.5. Bibliography ↑ Back to top

Nielsen, M. A. and Chuang, I. L. (2010). Quantum Computation and Quantum Information. Cambridge University Press.

Team, I. Q. (2023). Qiskit Textbook. IBM.

Möttönen, M. and Vartiainen, J. (2023). Quantum Computing: From Qubits to Quantum Machines. Springer.

IBM Research (2023). Ibm quantum hardware roadmap. Technical report, IBM Research. Accedido: 2026-02-13. La página original ha sido movida o actualizada.

Preskill, J. (2018). Lecture notes on quantum computation. Curso Ph219/CS219, California Institute of Technology. Material disponible en línea. La URL original http://theory.caltech.edu/~preskill/ph219/ no está operativa (febrero 2026). Se recomienda buscar la versión actual en el sitio web del autor.

Schuld, M. and Petruccione, F. (2021). Machine Learning with Quantum Computers. Springer, Cham, Switzerland, 2nd edition. Comprehensive introduction to quantum machine learning algorithms and implementations.

Bravyi, S., Dial, O., Gambetta, J. M., Gil, D., and Nazario, Z. (2022). Quantum algorithms for fixed qubit architectures. Nature Reviews Physics, 4(8):499–512. Survey on quantum algorithms for optimization and simulation with near-term devices.

Team, G. A. Q. (2019). Quantum supremacy using a programmable superconducting processor. Nature, 574.