PH3602: Quantum Information, Communication, and Computation

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Course Information

L-T-P-C3-0-0-3
Prerequisites None

Syllabus

Module 1: Basic Quantum Mechanics

Lecture hours: 20 · Tutorial hours: 0 · Lab hours: 0

Postulates of quantum mechanics, bra-ket notation, Linear algebra: state vectors, vector space and Hilbert space, matrices and operators, tensor product, Hamiltonian, evolution of state vectors, density matrix, pure and mixed states, Projection measurements, qubit and Bloch sphere, States and Hilbert spaces of multiple qubits, Trace, partial trace, and partial transposition .

Module 2: Quantum Gates and Circuits

Lecture hours: 4 · Tutorial hours: 0 · Lab hours: 0

Revisiting classical gates, Single-qubit quantum gates (X, Y, Z, H, T, and S gates), Basic quantum circuit diagrams, Controlled gates (controlled-X and controlled-Z gates) .

Module 3: Entanglement

Lecture hours: 5 · Tutorial hours: 0 · Lab hours: 0

Definition of entangled pure states, Schmidt decomposition, von Neumann entropy, Entangling gates, Entanglement in mixed states .

Module 4: Quantum Communication

Lecture hours: 4 · Tutorial hours: 0 · Lab hours: 0

No cloning theorem, Quantum dense coding, quantum teleportation, entanglement swapping, Basic quantum cryptography protocols (BB84 and Ekert protocol) .

Module 5: Quantum Error Correction

Lecture hours: 4 · Tutorial hours: 0 · Lab hours: 0

Single-qubit errors, Idea of quantum error detection and error correction, Correction of single-qubit bit-flip error .

Module 6: Quantum Algorithms

Lecture hours: 5 · Tutorial hours: 0 · Lab hours: 0

Introducing quantum parallelism and function evaluation, Deutsch-Jozsa algorithm, Grover's algorithm, Introduction to Shor's algorithm .

Study Materials

Textbooks

  1. Quantum Computation and Quantum Information, M. A. Nielsen and I. L. Chuang, Cambridge University Press (2007), ISBN: 978-81-7596-092-3
  2. Quantum Information Theory, M. M. Wilde, Cambridge University Press (2013), ISBN: 978-1107034259

References

  1. Lecture Notes by John Preskill (ph229, ph219), John Preskill, http://www.theory.caltech.edu/people/preskill/ph229/ ; http://www.theory.caltech.edu/~preskill/ph219/