Génie Quantique

Physics for Quantum Engineering

Description: This course introduces the fundamental concepts of quantum computing and the engineering of noisy quantum systems. It is intended for first-year Master’s students or second-year engineering students with a background in quantum mechanics and mathematical physics.

The course begins with a review of the basic principles of quantum computing. The concepts of qubits, superposition, entanglement, quantum gates, and quantum circuits are presented through simple examples and case studies based on current quantum technologies. An introduction to quantum algorithms is provided through emblematic protocols such as quantum teleportation.

The second part addresses the impact of noise on real quantum systems. The density matrix formalism is reviewed and used to describe open quantum systems and decoherence mechanisms. The main noise models and quantum channels are introduced, together with the concepts of relaxation, decoherence, and the characteristic time scales T1 and T2.

The third part focuses on the characterization and performance enhancement of quantum processors. Students are introduced to quantum tomography, benchmarking techniques, and modern error mitigation approaches. An introduction to quantum error correction is also provided through repetition codes and the stabilizer formalism.

Finally, the last part presents several numerical methods for simulating noisy quantum systems. Students are introduced to quantum circuit simulation, quantum trajectory methods, and tensor-network representations based on Matrix Product States. These concepts are reinforced through problem-solving sessions and programming-based practical exercises. .

Bibliography:

  • Ref1 : C. Gardiner and P. Zoller, Quantum noise (Springer-Verlag) (2004)
  • Ref2 : M. Joffre, Physique Quantique Avancée. Cours de lEcole Polytechnique (2023)
  • Ref3 : M.A. Nielsen I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2010)

Learning outcomes: AA1: Apply the fundamental formalisms of quantum information, including state vectors, density matrices, quantum gates, and quantum circuits, to describe the evolution of simple quantum systems. – AA2: Model and analyze the effects of noise, relaxation, and decoherence in open quantum systems using quantum channels and appropriate master-equation formalisms. – AA3: Explain the operating principles of current quantum computing technologies (NISQ devices) and identify the limitations arising from physical imperfections and noise. – AA4: Implement and interpret quantum error characterization, mitigation, and correction techniques, including tomography, benchmarking methods, and elementary quantum error-correcting codes.– AA5: Perform numerical simulations of noisy quantum systems and circuits, and analyze their performance using metrics such as fidelity, entanglement, and entropy.

Evaluation methods: Written Exam and Continuous Evaluation

Evaluated skills:

  • Physical Modeling

Course supervisor:

  • Thomas Tuloup
  • Corentin Bertrand
  • Baptiste Anselme Martin

Geode ID: SPM-PHY-016