**Exam Name:** Quantum Computing Fundamentals for Future Pioneers**Exam Time:** 3 Hours**Total Score:** 200**INSTRUCTIONS:**- This exam contains a total of 30 questions.- Answer all questions to the best of your ability.- The exam is closed book, closed notes, and no electronic devices are allowed.- Show all your work for calculation questions.- Circle the correct answer for multiple-choice questions.- Questions are worth different points, as indicated next to each question.- Only 40% of the questions will have answers provided.---**Question 1 (10 points):**What is the fundamental unit of information in a quantum computer?A. BitB. QubitC. ByteD. Nibble---**Question 2 (5 points):**Explain the concept of superposition in quantum computing and its significance.---**Question 3 (15 points):**Calculate the number of qubits required to represent \(2^{1024}\) states.---**Question 4 (20 points):**Discuss the principle of entanglement in quantum mechanics and its role in quantum computing.---**Question 5 (10 points):**
What is a quantum gate and how does it differ from a classical logic gate?---**Question 6 (5 points):**Which of the following is NOT a type of quantum gate?A. Pauli-X gateB. Hadamard gateC. Toffoli gateD. CNOT gate---**Question 7 (15 points):**Using the principles of quantum mechanics, explain how a quantum computer can perform parallel computations.---**Question 8 (10 points):**State the Church-Turing thesis and discuss how quantum computing challenges it.---**Question 9 (20 points):**Draw the circuit representation of a Deutsch-Josza algorithm for a function \(f: \{0,1\}^n \rightarrow \{0,1\}\).---**Question 10 (5 points):**True or False: Quantum computers can solve NP-complete problems in polynomial time.---**Question 11 (15 points):**Describe the process of quantum teleportation and its significance in quantum communication.---**Question 12 (10 points):**
What is quantum decoherence, and how does it pose a challenge to the operation of quantum computers?---**Question 13 (5 points):**Which of the following is NOT a method to reduce quantum decoherence?A. Cooled environmentsB. Quantum error correctionC. SuperpositionD. Isolation---**Question 14 (20 points):**Explain the Quantum Fourier Transform (QFT) and its applications in quantum algorithms.---**Question 15 (10 points):**Calculate the probability of measuring the state \(|1\rangle\) after applying a Hadamard gate to \(|0\rangle\).---**Question 16 (15 points):**Discuss the importance of the Grover's algorithm in quantum computing and its computational complexity.---**Question 17 (10 points):**What is the key advantage of Shor's algorithm over classical algorithms for factoring large numbers?---**Question 18 (5 points):**True or False: Quantum key distribution (QKD) provides absolute security in data transmission.---
**Question 19 (15 points):**Explain the role of quantum circuits in the execution of quantum algorithms.---**Question 20 (10 points):**Define a qubit in terms of its state representation.---**Question 21 (5 points):**Which of the following is NOT a known quantum advantage problem?A. Quantum random walkB. Quantum machine learningC. Quantum simulationD. Quantum factoring---**Question 22 (20 points):**Describe the principles behind quantum entanglement swapping and its potential applications.---**Question 23 (10 points):**Explain how quantum computing can potentially change the landscape of cryptography.---**Question 24 (15 points):**Discuss the potential impact of quantum computing on the future of artificial intelligence.---**Question 25 (10 points):**Define the term "quantum supremacy" and discuss its significance in the development of quantum computers.---
**Question 26 (5 points):**True or False: Quantum computers are expected to be faster than classical computers for all types of computations.---**Question 27 (15 points):**Explain the concept of quantum entanglement and its role in the teleportation of quantum states.---**Question 28 (10 points):**State the significance of the Toffoli gate in the context of quantum computing.---**Question 29 (5 points):**Which of the following is NOT a potential application of quantum computing?A. Drug discoveryB. Climate modelingC. Quantum encryptionD. Quantum gaming---**Question 30 (20 points):**Calculate the number of different quantum states that can be represented by \(n\) qubits.---**Answers for Selected Questions:****Question 1:**B. Qubit**Question 6:**C. Toffoli gate**Question 13:**C. Superposition
**Question 16:**Quantum key distribution (QKD) provides absolute security in data transmission.**Question 19:**Quantum circuits are the fundamental building blocks used to implement quantum algorithms, allowing for the manipulation of quantum bits (qubits) and the application of quantum gates to perform computations.**Question 21:**D. Quantum gaming**Question 25:**Quantum supremacy is the milestone at which a quantum computer can perform a task that no classical computer can complete in a reasonable amount of time.**Question 27:**Quantum entanglement allows the teleportation of quantum states without the need for a physical particle to travel through space, which is significant for quantum communication and computation.**Question 30:**\(2^n\)