Course

Unit 1

Introduction to Quantum Computing and Noise: Overview of Quantum Computing, Quantum fragility and decoherence, Quantum Noise: Sources of noise in quantum systems, including depolarizing, bit-flip, and phase-flip errors.

Unit 2

Quantum Error Correction: Knill-Laflamme Conditions, Repetition Code, Steane and Shor Codes, Five Qubit Code.

Unit 3

Stabilizer Codes and Passive Error Correction: Stabilizer Codes, Pauli Groups, CSS Codes, Decoherence Free Subspaces.

Unit 4

Fault-Tolerant Quantum Computing and Topological Codes Fault-Tolerance, Error Threshold Theorem, Topological error-correcting codes, Surface Code.

Course Objectives:

• Gain a thorough understanding of the core concepts of quantum error correction, emphasizing the sources of quantum noise, the effects of decoherence, and the challenges involved in preserving the reliability of quantum information.
• Learn and apply various quantum error correction codes including the stabilizer codes with an emphasis on their practical application in error detection and correction within quantum systems.
• Explore the principles and techniques for fault-tolerant quantum computing, to ensure the robustness and resilience of quantum computations in the face of noise and system imperfections.

Course Outcomes (COs):

CO1: Understand the basic principles of quantum computing and the sources of noise in quantum systems.

CO2: Analyse the challenges faced in quantum computing, including decoherence and fragility, and apply quantum error correction techniques.

CO3: Construct and implement quantum error correction methods based on stabilizer codes with a focus on their application in error detection and correction.

CO4: Apply fault-tolerant quantum computing techniques and understand topological error-correcting codes.

CO-PO Mapping:

Evaluation Pattern: 50:50

*CAT – Can be Quizzes/Assignments

*CAL – Can be Lab Assessments/Project/ Report

Reference(s)

• Nielsen MA, Chuang IL. “Quantum computation and quantum information”. Cambridge University Press.
• Lidar and T. Brunn, “Quantum Error Correction”, Cambridge University Press.