Quiz: Why Quantum Computing?

This quiz checks the main ideas from Chapter 1. It focuses on concepts rather than calculation.

Questions

1. Quantum computing as a model

Which statement best describes why quantum computing is different from ordinary classical computing?

A. Quantum computers use smaller transistors. B. Quantum computers are classical computers built from quantum materials. C. Quantum computers represent and manipulate information using quantum states. D. Quantum computers are just faster versions of ordinary computers.

2. Classical hardware and quantum mechanics

Why is it not enough to say that a computer is “quantum” merely because its hardware relies on quantum physics?

A. Classical computers do not use quantum physics at all. B. Many classical devices rely on quantum effects, but still store and process information as classical bits. C. Quantum physics only matters for communication, not computation. D. Quantum hardware always performs analog computation.

3. Bits and qubits

A classical bit can have value 0 or 1. A qubit can be in a state of the form:

A. 0 + 1 B. a|0> + b|1> C. a x 0 + b x 1, where a and b are probabilities D. either |0> or |1>, but never anything else

4. Amplitudes and probabilities

If a qubit is in the state

1a|0> + b|1>

and is measured in the standard basis, what is the probability of observing 0?

A. a B. b C. |a|^2 D. |b|^2

5. Measurement

Which statement about quantum measurement is correct?

A. Measurement reveals the full quantum state. B. Measurement usually changes the quantum state. C. Measurement allows us to copy an unknown qubit. D. Measurement always gives the same result regardless of basis.

6. Repeated measurement

Suppose a qubit is measured in the standard basis and the outcome is 0. If it is immediately measured again in the same basis, what happens?

A. The result is definitely 0. B. The result is definitely 1. C. The result is equally likely to be 0 or 1. D. The original amplitudes are recovered.

7. Superposition

Why is it misleading to say that a qubit in superposition is “just a probabilistic bit”?

A. A probabilistic bit can never be measured. B. A qubit has phase information and can show interference effects. C. A probabilistic bit always stores more information than a qubit. D. A qubit cannot produce random-looking measurement outcomes.

8. Phase

The two states

11/sqrt(2) (|0> + |1>)

and

11/sqrt(2) (|0> - |1>)

give the same probabilities when measured in the standard basis. Why are they still different quantum states?

A. They use different basis states. B. They have different relative phases. C. One is classical and the other is quantum. D. They represent the same state in all circumstances.

9. Quantum parallelism

A register of n qubits can be placed in a superposition involving how many standard basis states?

A. n B. 2n C. 2^n D. infinitely many measurement outcomes

10. Limits of quantum parallelism

Why does quantum parallelism alone not give an automatic exponential speedup?

A. Superpositions cannot be created. B. Quantum computers cannot apply functions to superpositions. C. Measurement gives only limited classical information. D. Classical computers can already measure all branches of a superposition.

11. Interference

What role does interference play in quantum algorithms?

A. It prevents quantum computers from using superposition. B. It allows amplitudes for some outcomes to reinforce and others to cancel. C. It turns qubits into classical bits before measurement. D. It removes the need for measurement.

12. Entanglement

Which state is an example of an entangled two-qubit state?

A. |00> B. |0>|1> C. 1/sqrt(2) (|00> + |11>) D. 1/sqrt(2) (|0> + |1>)

13. Entanglement as a resource

Why is entanglement important in quantum information processing?

A. It makes every quantum algorithm exponentially faster. B. It allows joint quantum states that cannot be described by separate states of the parts. C. It lets us read all amplitudes directly. D. It removes the need for error correction.

14. Quantum computing and hype

Which statement is most accurate?

A. Quantum computers efficiently solve all hard problems. B. Quantum computers are expected to replace all classical computers. C. Quantum computers offer advantages for some specialized tasks. D. Quantum computers are useful only because they are physically smaller.

15. Shor’s algorithm

Why was Shor’s algorithm important?

A. It showed that quantum computers can solve every search problem instantly. B. It gave a polynomial-time quantum algorithm for factoring integers. C. It proved that classical computers cannot factor integers. D. It removed the need for quantum error correction.

16. Grover’s algorithm

Grover’s algorithm gives what kind of speedup for unstructured search?

A. No speedup B. Linear speedup C. Quadratic speedup D. Exponential speedup

17. Limits shown by Grover’s algorithm

Why is Grover’s algorithm also an example of a limitation of quantum computing?

A. It works only on classical computers. B. Its quadratic speedup is known to be the best possible for unstructured search. C. It requires no qubits. D. It solves factoring but not search.

18. Quantum simulation

Why is quantum simulation a natural application of quantum computers?

A. Quantum systems are always easy to simulate classically. B. Quantum computers are themselves quantum systems. C. Quantum simulation requires no measurement. D. Quantum simulation avoids the use of amplitudes.

19. Decoherence

What is decoherence?

A. A method for copying unknown quantum states. B. A quantum algorithm for factoring. C. The loss of quantum behavior through unwanted interaction with the environment. D. The process of converting classical bits into transistors.

20. Quantum error correction

Why is quantum error correction surprising?

A. Classical information cannot be protected from errors. B. It protects quantum information even though unknown quantum states cannot simply be copied. C. It works by measuring the full quantum state directly. D. It proves that decoherence does not occur.

Short answer questions

21. Model versus hardware

In two or three sentences, explain why quantum computing should be understood as a new model of computation rather than merely a new hardware technology.

22. Measurement

Explain why measurement limits the amount of classical information we can extract from a quantum state.

23. Superposition and interference

What is the difference between creating a superposition and using that superposition effectively in a quantum algorithm?

24. Entanglement

Explain why the state

11/sqrt(2) (|00> + |11>)

cannot be understood as simply “the first qubit has a state and the second qubit has a state.”

25. Limits of quantum computing

Give one example of a task where quantum computers are known to offer an advantage, and one reason why this does not mean they solve all computational problems efficiently.

Applied questions

26. Measurement simulation

The following code simulates repeated measurements with fixed probabilities:

 1import random
 2from collections import Counter
 3
 4def measure_qubit(prob_zero, shots=1000):
 5    results = []
 6
 7    for _ in range(shots):
 8        if random.random() < prob_zero:
 9            results.append(0)
10        else:
11            results.append(1)
12
13    return Counter(results)

Why is this not yet a full qubit simulation?

27. Same probabilities, different states

Suppose two qubit states give the same probabilities when measured in the standard basis. Does that mean they are the same quantum state? Explain briefly.

28. Quantum advantage

A student says:

A quantum computer can evaluate a function on every input at once, so it can always solve problems exponentially faster.

What is wrong with this statement?

29. Cryptography

Why did Shor’s algorithm attract attention outside physics and computer science theory?

30. Course roadmap

Which topics from later in the course are needed to fully understand Shor’s algorithm?

A good answer should mention several of the following:

• qubits,
• quantum gates,
• reversible computation,
• quantum circuits,
• quantum Fourier transforms,
• period finding,
• measurement.

Answer key

Multiple choice

Short answer guidance

21. Model versus hardware

A good answer should say that classical computers may use quantum effects in their physical components, but they still encode and manipulate information as classical bits. Quantum computers use qubits and quantum transformations, so the model of information itself changes.

22. Measurement

A good answer should mention that measurement produces a limited classical outcome and usually changes the quantum state. A single qubit measurement gives at most one classical bit of information, not the full amplitudes.

23. Superposition and interference

A good answer should distinguish putting many basis states into a superposition from arranging amplitudes so that useful outcomes become likely. Quantum algorithms need interference, not just superposition.

24. Entanglement

A good answer should say that the joint state cannot be factored into a state of the first qubit times a state of the second qubit. The system has correlations that belong to the pair as a whole.

25. Limits of quantum computing

Examples of quantum advantages include Shor’s algorithm for factoring, Grover’s algorithm for search, or quantum simulation. A good limitation should say that quantum speedups are specialized, and some problems have no known quantum speedup or only limited speedup.

Applied question guidance

26. Measurement simulation

The code only simulates classical random outcomes with fixed probabilities. It does not represent complex amplitudes, phase, change of basis, unitary transformations, interference, or entanglement.

27. Same probabilities, different states

No. States can have the same measurement probabilities in one basis but differ by relative phase. They may behave differently under later transformations or measurements in another basis.

28. Quantum advantage

The statement ignores measurement. Even if a superposition contains amplitudes associated with many inputs, measuring reveals only limited information. Quantum algorithms need interference to amplify useful information.

29. Cryptography

Shor’s algorithm showed that a large reliable quantum computer could factor integers efficiently, threatening cryptographic systems such as RSA that rely on the apparent classical difficulty of factoring.

30. Course roadmap

A good answer should mention that Shor’s algorithm requires the machinery of qubits, quantum gates and circuits, reversible computation, quantum Fourier transforms, period finding, and measurement.