(SEM VII) THEORY EXAMINATION 2024-25 QUANTUM COMPUTING

QUANTUM COMPUTING (KCS710)

Time: 3 Hours | Maximum Marks: 100

SECTION A (10 × 2 = 20 Marks)

(Attempt all questions in brief)

1(a) Discuss the evolution of quantum information as a field.

Quantum information evolved from quantum mechanics and information theory. Early work by Shannon laid foundations of classical information, while later contributions by Feynman and Deutsch introduced quantum computation. The field now includes quantum algorithms, communication, cryptography, and error correction.

1(b) Elaborate on the probability amplitudes’ impact on measurement outcomes.

Probability amplitudes are complex numbers whose squared magnitudes give measurement probabilities. Interference between amplitudes determines constructive or destructive outcomes, directly influencing observable results.

1(c) Explore applications of quantum algorithms in solving NP-complete problems.

Quantum algorithms like Grover’s algorithm provide quadratic speedup for search problems related to NP-complete classes. While quantum computers do not yet solve NP-complete problems efficiently, they significantly reduce search complexity.

1(d) Analyze the effect of decoherence on quantum search algorithms.

Decoherence causes loss of superposition and phase information, reducing quantum interference. In quantum search algorithms, this degrades success probability and eliminates speedup advantages.

1(e) How are photons manipulated within optical cavities for computation?

Photons are confined using mirrors in optical cavities. Their states are manipulated using beam splitters, phase shifters, and nonlinear media to implement quantum gates for photonic quantum computing.

1(f) Discuss the principles of NMR-based quantum computing.

NMR quantum computing uses nuclear spins as qubits. Radio-frequency pulses control spin states, while ensemble measurements detect outcomes. It offers precise control but limited scalability.

1(g) Discuss the sources of quantum noise.

Quantum noise arises from environmental interactions, thermal fluctuations, imperfect gate operations, measurement errors, and decoherence processes like amplitude damping and phase damping.

1(h) Discuss the impact of quantum decoherence on quantum computation and communication protocols.

Decoherence reduces coherence and entanglement, causing computational errors and loss of secure communication. It limits algorithm reliability and transmission fidelity.

1(i) Discuss implementation of fault tolerance in quantum circuits.

Fault tolerance is achieved using quantum error-correcting codes, logical qubits, syndrome measurement, and fault-tolerant gate constructions that prevent error propagation.

1(j) Discuss challenges of implementing quantum error correction in NISQ devices.

NISQ devices suffer from limited qubit count, high noise, imperfect gates, and measurement errors, making large-scale error correction resource-intensive and difficult.

SECTION B (Attempt any THREE) (3 × 10 = 30 Marks)

2(a) Explain quantum superposition and entanglement and their role in computation.

Superposition allows qubits to exist in multiple states simultaneously. Entanglement creates strong correlations between qubits. Together, they enable quantum parallelism and exponential state space exploration beyond classical limits.

2(b) Deutsch–Jozsa algorithm: circuit and explanation.

The algorithm uses Hadamard gates to evaluate a function in one query. A quantum circuit prepares superposition, applies oracle evaluation, and interference reveals whether the function is constant or balanced, demonstrating quantum parallelism.

2(c) Ion-trap quantum computer architecture.

Ions are trapped using electromagnetic fields. Laser pulses initialize, manipulate, and entangle qubits. Measurement is done via fluorescence detection. Ion traps provide high fidelity but face scalability challenges.

2(d) Quantum operations and Kraus operator formalism.

Quantum operations describe open system evolution.
State transformation:

ρ′=∑kEkρEk†\rho' = \sum_k E_k \rho E_k^\daggerρ′=k∑​Ek​ρEk†​

Kraus operators model noise such as depolarization and amplitude damping.

2(e) Shannon entropy derivation and its role.

Shannon entropy is given by:

H(X)=−∑p(x)log⁡p(x)H(X) = -\sum p(x)\log p(x)H(X)=−∑p(x)logp(x)

It measures information uncertainty and is fundamental to classical and quantum data compression limits.

SECTION C (Attempt any ONE) (10 Marks)

3(a) Quantum mechanics postulates and implications for computation.

Postulates define state vectors, measurement collapse, unitary evolution, and composite systems. They enable superposition, entanglement, and probabilistic outcomes essential for quantum algorithms.

3(b) Role of interference and superposition in quantum speedup.

Quantum algorithms amplify correct solutions via constructive interference and suppress incorrect ones through destructive interference, enabling exponential or quadratic speedups.