(SEM VII) THEORY EXAMINATION 2023-24 QUANTUM COMPUTING

KCS710 – QUANTUM COMPUTING

Section-wise Solved Answers

SECTION A (2 × 10 = 20 Marks)

Attempt all questions in brief

a) Superposition

Superposition is a fundamental principle of quantum computing in which a qubit can exist in multiple states (0 and 1) simultaneously until it is measured.

b) Qubits vs Classical Bits

A classical bit can be either 0 or 1, whereas a qubit can be in a superposition of both 0 and 1 at the same time, allowing parallel computation.

c) Quantum Gates

Quantum gates are unitary operations that manipulate qubits. They change the probability amplitudes of quantum states and form the building blocks of quantum circuits.

d) Significance of Quantum Algorithms

Quantum algorithms solve certain problems much faster than classical algorithms, providing exponential or polynomial speedup.

e) Basic Components of a Quantum Computer

Qubits                                                                        Quantum gates

Quantum circuits                                                       Measurement system

Classical control system

f) Ion Trap

An ion trap uses electromagnetic fields to trap charged atoms (ions) and uses them as qubits for quantum computation.

g) Quantum Noise

Quantum noise refers to unwanted disturbances in quantum systems that cause errors due to decoherence and interaction with the environment.

h) Distance Measures for Quantum Information

Distance measures quantify the difference between quantum states, such as trace distance and fidelity.

i) Stabilizer Codes

Stabilizer codes are quantum error-correcting codes that protect quantum information using group theory and Pauli operators.

j) Shor Code

The Shor code is a 9-qubit quantum error-correcting code used to protect against both bit-flip and phase-flip errors.

SECTION B (Attempt Any Three – 10 Marks Each)

a) Principles and Computational Models of Quantum Computation

Underlying Principles:                                        Superposition

Entanglement                                                       Quantum interference

Measurement

Computational Models:                                     Quantum circuit model

Adiabatic quantum computing                            Measurement-based quantum computing

These models enable parallelism and speedup over classical computation.

b) Quantum Gates and Their Role

Quantum gates perform state transformations on qubits.

Types of Quantum Gates:

Single-qubit gates: Pauli-X, Y, Z, Hadamard

Multi-qubit gates: CNOT, Toffoli

Role:
They form quantum circuits and implement quantum algorithms.

c) Harmonic Oscillator Quantum Computer

A harmonic oscillator quantum computer uses quantized energy levels of oscillators as qubits.

Significance:

Useful in continuous-variable quantum computing

Supports quantum simulations

Helps in quantum information processing

d) Markov Processes and Quantum Noise

Markov processes describe systems where future states depend only on the present state.

Role in Quantum Noise:

Model decoherence

Describe memory-less noise

Affect stability and reliability of quantum operations

e) Quantum Error-Correcting Codes

Methodologies:

Encoding logical qubits into physical qubits

Syndrome measurement

Error detection and correction

Considerations:                                                                 Noise models

Fault tolerance                                                                    Resource efficiency

SECTION C (Attempt Any One – 10 Marks)

a) Significance of Quantum Algorithms

Examples:

Shor’s algorithm (factorization)                                        Grover’s algorithm (search)

Significance:                                                                     Faster problem solving

Cryptography breaking                                                     Optimization and simulation

b) Postulates of Quantum Mechanics                               State vector postulate

Measurement postulate                                                    Time evolution (Schrödinger equation)

Composite systems

These postulates define how quantum systems behave.

SECTION D (Attempt Any One – 10 Marks)

a) Quantum Circuits

Quantum circuits consist of qubits, quantum gates, and measurements.

Role:

Implement quantum algorithms

Control quantum state evolution

b) Quantum Speedup

Quantum speedup refers to performance improvement over classical computers.

Examples:

Shor’s algorithm

Grover’s algorithm