QUANTUM COMPUTING (Professional Elective – IV) B.Tech. IV Year I Sem. JNTUH R-18

• Explain how concepts like vectors, matrices, and set theory lay the foundation for understanding quantum mechanics.

• Demonstrate how complex numbers are essential for representing quantum states and performing calculations.

• Describe the properties of Pauli matrices and their role in representing quantum gates.

• Differentiate between transcendental and algebraic numbers in the context of quantum computing.

Unit II: Basic Physics for Quantum Computing

• Discuss the key differences between classical and quantum physics, highlighting the concept of uncertainty.

• Explain the concept of Hilbert spaces and their role in representing quantum states.

• Describe the phenomenon of entanglement and its implications for quantum algorithms.

• Compare and contrast different interpretations of quantum mechanics, such as the Copenhagen interpretation and the Many-Worlds interpretation.

Unit III: Quantum Architecture

• Explain the difference between a qubit and a classical bit, and discuss the challenges of physical qubit implementation.

• Describe the key elements of quantum circuits, including quantum gates and measurement operations.

• Analyze the architecture of the D-Wave quantum computer and its strengths and limitations.

• Discuss the challenges of decoherence and various approaches to address it in quantum hardware.

Unit IV: Quantum Algorithms

• Explain the concept of an algorithm and how it applies to quantum computing.

• Analyze the Deutsch-Jozsa algorithm and its ability to solve the hidden subset problem efficiently.

• Discuss the Bernstein-Vazirani algorithm and its application to period finding.

• Describe Simon's algorithm and its use for factoring integers.

• Explain the power of Shor's algorithm for breaking RSA encryption.

• Analyze Grover's search algorithm and its quadratic speedup compared to classical search algorithms.

Unit V: Current Asymmetric Algorithms and Impact on Cryptography

• Explain the principles of popular asymmetric cryptographic algorithms like RSA, Diffie-Hellman, and elliptic curve cryptography.

• Analyze the vulnerability of these algorithms to attacks from quantum computers with specific examples.

• Discuss the potential impact of quantum computing on existing cryptographic infrastructure and potential solutions for post-quantum cryptography.