Basic Linear Algebra

• • • a. Idea of vector space and subspace, Row and column vector, linear combination of vectors and spanning set, Basis and dimensions, Inner products, Orthonormality and Gram-Schmidt orthogonalization, Bra-ket formalism, Cauchy-Schwarz and Triangle inequality

    • b. Linear operators and their matrix representation, Outer products, Hermitian (Self-adjoint), unitary, normal operators, Eigenvalue and eigenvectors, Diagonalization, Trace, expectation values, Commutator of two operators

    • c. Tensor product or Kronecker product of column vectors and Matrices

    • Refer to Chapters 2, 3, and 4 of Quantum Computing Explained by David McMahon. These chapters introduce the key concepts in a clear and accessible manner, supported by illustrative examples

• Basic Quantum Mechanics

  • • a. Postulates of Quantum Mechanics: Familiarity with quantum state, measurement of an observable, and unitary evolution of a quantum state

Lecture 1 : Motivation, Quantum Three-bit repetition code for correcting bit and phase flip error (1 hour)

Lecture 2 : Concatenation and nine qubit Shor code. Introducing some of the fundamental concepts of quantum information theory: Density matrix, POVMs (1 hour)

Lecture 3 : Quantum Channels (1 hour)

Lecture 4 : Fundamental theory of quantum error correction: Proving Knill Laflamme condition (1 hour)

Lecture 5 : Discretization of error, independent error models, The quantum Hamming bound (1 hour)

Lecture 6 : Constructing quantum code : Classical Linear code I (1 hour)

Lecture 7 : Constructing quantum code : Classical Linear code II (1 hour)

Lecture 8 : Calderbank Shor Steane code (1 hour)

Lecture 9 : Introduction to the stabilizer formalism (1 hour)

Lecture 10 : Stabilizer code I (1 hour)

Lecture 11 : Stabilizer code II (1 hour)

Lecture 12 : Guest lecture by Dr. Vivek Sinha, QuTech, TU Delft, Netherlands (1 hour)

Lecture 13 : Quiz and doubt clearance (1 hour)