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Course Detail

Course Name Mathematical Foundations for Quantum Computing
Course Code 26QTS231M
Credits 4
Campus Amaravati, Amritapuri, Bengaluru, Coimbatore, Chennai

Syllabus

Syllabus

Complex Numbers: Introduction – complex conjugate, Euler’s formula and polar form, Vectors, Complex vector spaces and state representation – norms and orthogonality, Dirac notation, Hilbert spaces, Matrices and operations, conjugate transpose and inverse, Unitary, Hermitian, and Normal matrices, Eigenvalues and eigenvectors, Density Matrix, Inner product, Outer product, Tensor product, Probability amplitudes, normalization and measurement probabilities, Postulates of Quantum Mechanics, Fourier transform: Quantum states and Transformations, Qubit, representation in Bloch Sphere.

Objectives and Outcomes

Course Objectives

  1. Understand mathematical foundations of quantum Computing including complex numbers and vector spaces.
  2. To learn linear algebra and matrix operations used in quantum state representation.
  3. Understand quantum mechanics postulates, probability amplitudes, and tensor products.
  4. Understand the qubits using Bloch sphere and Fourier transform and quantum state transformations.

Course Outcomes

  • CO1: Demonstrate the use of complex numbers, vector spaces, Dirac notation, and Hilbert spaces in representing quantum states.
  • CO2: Apply matrices, eigenvalues, density matrices, and tensor products in quantum systems.
  • CO3: Analyze the probability amplitudes and postulates of quantum mechanics for measurement and state evolution.
  • CO4: Represent qubits and quantum transformations using Fourier transform and Bloch sphere.

CO-PO Mapping

PO/PSO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO 9

PO10

PO11

PSO1

PSO2

CO

CO1

3

2

–

–

1

–

–

–

–

–

1

2

3

CO2

3

3

–

2

2

–

–

–

–

–

1

2

1

CO3

3

2

1

2

2

–

–

–

–

–

1

1

2

CO4

2

2

2

1

3

–

–

–

1

–

2

1

2

Evaluation Pattern

Evaluation Pattern : 70:30

Assessment Internal/External Weightage (%)
Assignments (Minimum 2) Internal 30
Quizzes (Minimum 2) Internal 20
Mid-Term Examination Internal 20
Term Project / End Semester Examination External 30

Text Books / References

EXTBOOKS

  1. William (Chuck) Easttom, Quantum Computing Fundamentals, Pearson Education (US). 2021
  2. Helmut Bez, Tony Croft, Quantum Computation- 1st Edition, Chapman & Hall publication, 2023
  3. Rajendra K. Bera, The Amazing World of Quantum Computing, Springer, 2020.

REFERENCE BOOKS

  1. Michael A. Nielsen & Isaac L. Chuang, Quantum Computation and Quantum Information , Cambridge University Press, 2010
  2. Mikio Nakahara and Tetsuo Ohmi, Quantum Computing: From Linear Algebra to Physical Realizations, 1st Edition, CRC Press, 2008.
  3. Griffiths, D. J. and Schroeter, D. F, Introduction to Quantum Mechanics, 3rd Edition, Cambridge University Press, 2020.

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