Self-Assessment Quiz: Multi-Qubit Programming

Twenty questions on tensor products, CNOT, entanglement, and what hardware does to all of it. Aim for 16 or more.

Question 1

An $n$-qubit state requires how many complex amplitudes? - A. $n$ - B. $2n$ - C. $n^2$ - D. $2^n$

Question 2

In Qiskit's ordering, qubit 0 appears: - A. first in the tensor product (leftmost in the bitstring) - B. last in the tensor product (rightmost in the bitstring) - C. in the middle - D. it depends on the circuit

Question 3

A 2-qubit circuit with h(1) applied puts amplitude on which array indices? - A. 0 and 1 - B. 0 and 2 - C. 1 and 2 - D. 2 and 3

Question 4

After cx(0, 1), the input '01' becomes: - A. '01' - B. '10' - C. '11' - D. '00'

Question 5

A state that can be written $|a\rangle \otimes |b\rangle$ is called: - A. entangled - B. a product state - C. a Bell state - D. mixed

Question 6

How many numbers describe a product state of $n$ qubits? - A. $2^n$ - B. $2n$ - C. $n!$ - D. $n^2$

Question 7

h(0); cx(0, 1) produces: - A. all four outcomes at 25% each - B. 00 and 11 at 50% each - C. 01 and 10 at 50% each - D. 00 with certainty

Question 8

The reduced state of one qubit of a Bell state has purity: - A. 1.0 - B. 0.5 - C. 0.0 - D. 0.25

Question 9

The Bloch vector of one qubit of a Bell state has length: - A. 1.0 - B. 0.707 - C. 0.5 - D. 0.0

Question 10

That Bloch length means the qubit is: - A. in an equal superposition - B. at the center of the sphere — completely undetermined on its own - C. in the state $|0\rangle$ - D. in an invalid state

Question 11

Two circuits produce identical {'00': 50%, '11': 50%} counts. You can conclude: - A. both are entangled - B. neither is entangled - C. nothing about entanglement — you need a second measurement basis - D. both contain a CNOT

Question 12

Which pair of Bell states is indistinguishable by computational-basis measurement? - A. $|\Phi^+\rangle$ and $|\Psi^+\rangle$ - B. $|\Phi^+\rangle$ and $|\Phi^-\rangle$ - C. $|\Psi^+\rangle$ and $|\Phi^-\rangle$ - D. all four are distinguishable

Question 13

A Bell measurement is performed by: - A. measuring both qubits twice - B. applying the inverse of the Bell preparation before measuring - C. measuring one qubit and inferring the other - D. using a special hardware instruction

Question 14

A SWAP gate costs how many CNOTs? - A. 1 - B. 2 - C. 3 - D. 6

Question 15

A Toffoli gate costs how many CNOTs? - A. 2 - B. 3 - C. 6 - D. 14

Question 16

Why does the SWAP cost matter even though you rarely write swap? - A. It does not; it is a curiosity - B. The transpiler inserts SWAPs automatically to route between non-adjacent qubits - C. SWAP is used in every measurement - D. Because SWAP is not universal

Question 17

CZ differs from CNOT in that CZ is: - A. not a two-qubit gate - B. symmetric — no control/target distinction - C. not unitary - D. only available in simulation

Question 18

Losing one qubit of a 3-qubit GHZ state leaves the other two: - A. still maximally entangled - B. in a classical mixture with no entanglement - C. in a pure product state - D. in a W state

Question 19

Which is true of an algorithm that generates no substantial entanglement? - A. It runs faster on hardware - B. It is classically simulable and cannot give a quantum advantage - C. It is more accurate - D. It requires more qubits

Question 20

In the chapter's hardware experiment, GHZ fidelity collapsed at $n=7$ under optimization level 1 because: - A. seven qubits is the coherence limit - B. the chain reached a broken physical qubit with a gate error of 1.0 - C. the simulator ran out of memory - D. GHZ states are undefined above six qubits

Answers

# Answer Why
1 D The tensor product multiplies dimensions. §4.1
2 B Little-endian — the reverse of most textbooks. §4.1
3 B Index 2 is '10', i.e. qubit 1 is set. §4.2 pitfall
4 C Control $q_0$ is 1, so target $q_1$ flips. §4.2
5 B Both qubits have their own state. §4.1
6 B Two per qubit — which is why product states are trivially simulable. §4.1
7 B The Bell state $\lvert\Phi^+\rangle$. §4.3
8 B 0.5 is the floor for a single qubit: maximally mixed. §4.4
9 D Zero. §4.4
10 B Not "in superposition" — superposition is pure and has definite phases. §4.4
11 C A classically conditioned circuit gives identical counts. §4.4 pitfall
12 B $\Phi$ vs $\Psi$ shows in the counts; the $\pm$ does not. §4.5
13 B Rotate into the basis where the states differ, then measure. §4.5
14 C Three. §4.6
15 C Six, with all-to-all connectivity assumed. §4.6
16 B The largest hidden cost in quantum programming. §4.6
17 B Which is why some hardware uses cz natively. §4.6
18 B GHZ is fragile; W is robust. §4.7
19 B Entanglement is the resource, not decoration. §4.8
20 B Readout error 0.257 and ECR error 1.0 on physical qubit 6. §4.9

Topic Map

Questions Topic Section If you missed these
1, 2, 3, 6 Tensor product and endianness §4.1, §4.2 Do Exercise 4.7. Endianness causes more bugs than anything else in the book
4, 7 CNOT §4.2, §4.3 Trace the truth table by hand once
5, 8, 9, 10, 11 What entanglement is §4.4 The conceptual core. Run code/example-02-bell-states-and-entanglement.py
12, 13 The four Bell states §4.5 Exercise 4.10; the Bell measurement recurs in Chapter 9
14, 15, 16, 17 Gate costs §4.6 Memorize SWAP = 3, Toffoli = 6. They govern Part IV's feasibility
18 GHZ vs W §4.7 Exercise 4.13 — read the eigenvalues, not just the entropy
19 Why entanglement matters §4.8 The single best filter for evaluating quantum advantage claims
20 Hardware reality §4.9 Do Exercises 4.20–4.22; the layout lesson is worth an hour

Score 16+: go to Chapter 5.

Score 12–15: check which cluster you lost. Questions 8–11 are the ones that matter most; if you missed those, reread §4.4 and run the entanglement report on both a product state and a Bell state with your own hands.

Score under 12: the gate-cost trivia (14–17) is reference you can look up. The concepts to fix before Chapter 5 are: little-endian ordering (2, 3), what CNOT does to a superposition (4, 7), and that counts alone never establish entanglement (11).