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
