Syllabus
Unit 1
Introduction to quantum mechanics from a QI/QC perspective: Classical information storage and bits, quantum states and qubits, vector spaces, basis, inner product, adjoint and dual vectors; Operators, and matrices, adjoint of operators; Hermitian, unitary and normal operators; Eigenvalues, eigenvectors, diagonalization, trace; Observables, measurement and expectation value of an operator; unitary transformations and change of basis; projection operators; positive operators, polar and singular value decompositions; commuting and non-commuting operators, uncertainty relations; a summary of postulates of quantum mechanics, unitary evolution of quantum states, rotation of spin states and Bloch sphere representations.
Unit 2
Many-particle composite states and tensor products. Quantum Measurements: projective measurements of simple and composite systems, generalized measurements, positive operator-valued measures (POVMs); experiments with IBM qiskit or equivalent platforms.
Unit 3
Entanglement: EPR ideas – nonlocality, Bell’s inequality, bipartite systems, Bell states, Schmidt decomposition; simulations and experiments with IBM qiskit.
Unit 4
Quantum Gates and Circuits: Classical logic gates, single cubit gates, basic quantum circuit diagrams, controlled gates, gate decomposition; experiments with IBM qiskit.
Unit 5
Quantum Algorithms: Hadamard gates, phase gate, series and parallel operations, function evaluation, Deutsch-Jozsa algorithm; Quantum teleportation, Superdense coding, no-cloning theorem; experiments with IBM qiskit.
Suggested lab exercises:
The lab exercises are based on implementing the quantum computational understanding in the IBM qiskit based simulations as well as on the Publicly available IBM quantum computers.
- IBM Qiskit, Quantum gates and basic quantum circuits, state preparation
Introduction to IBM Qiskit
Introduction to quantum gates and putting together simple gate circuits.
Preparation of desired states (up to three qubits) by using quantum gates.
- Quantum Measurements:
Implementing measurements and unitary gates.
Classical and quantum random number generation.
- Bipartite entanglement:
Bell state preparation and Bell state measurements; Verification of Bell inequalities.
- Deutsch-Jozsa algorithm.
- Quantum teleportation and Quantum superdense coding.
Description and Outcomes
Course Description
This course introduces the fundamentals of quantum computing through hands-on learning using IBM Qiskit and real quantum computers. Topics include quantum gates, circuits, and measurements. Lab exercises cover bipartite entanglement, Bell inequalities, the Deutsch-Jozsa algorithm, quantum teleportation, and superdense coding.
Course Outcomes
After successful completion of the course, students will be able to
- Apply mathematical tools to understand and solve problems related to essential principles of quantum mechanics for quantum information.
- Apply tensor product structures to construct and analyse multi-particle quantum states and quantum measurement operations, utilizing IBM Qiskit for demonstrations and validation.
- Demonstrate quantum entanglement and verify Bell’s inequality and Schmidt decomposition, incorporating experiments using IBM Qiskit.
- Apply principles of operation for quantum gates and circuits, performing gate decompositions and verifying operations using IBM Qiskit simulations.
- Explain and implement basic quantum algorithms and communication protocols (e.g., Deutsch-Jozsa, teleportation, quantum parallelism, and speed-up), and verify them utilizing IBM Qiskit.
