Self-Assessment Quiz: Measurement, Shots, and Statistics

Twenty questions on what measurement does, how much it costs, and what you are entitled to conclude from it. Aim for 16 or more.

Question 1

Measurement does which two things? - A. Returns a bit, and leaves the state unchanged - B. Returns a bit, and replaces the state with the corresponding basis state - C. Copies the state to a classical register - D. Reverses the last gate

Question 2

"Measurement happens in a basis" means: - A. measurement always returns 0 or 1 - B. the measurement is specified by a set of orthogonal states, and different choices give different answers - C. you must always use the computational basis - D. bases are a simulator-only concept

Question 3

$|+\rangle$ measured in the $X$ basis gives: - A. 50/50 - B. 0 with certainty - C. 1 with certainty - D. an error

Question 4

In the counts key '0110', qubit 0 measured: - A. 0 - B. 1 - C. cannot tell - D. both

Question 5

With two classical registers a (declared first) and b (declared second), the counts key looks like '00 1'. Which part is b? - A. the right part, 1 - B. the left part, 00 - C. they are interleaved - D. registers are always merged

Question 6

The standard error of a probability estimated from $N$ shots is at most: - A. $1/N$ - B. $1/\sqrt{N}$ - C. $1/(2\sqrt{N})$ - D. $1/N^2$

Question 7

To improve precision by a factor of 10, shots must increase by a factor of: - A. 10 - B. 100 - C. 2 - D. 1000

Question 8

Roughly how many shots for a precision of ±0.01 at 95% confidence? - A. 100 - B. 1,000 - C. 9,600 - D. 960,000

Question 9

The $1/\sqrt{N}$ scaling is: - A. a limitation of NISQ hardware that error correction will fix - B. the statistics of sampling, which a perfect quantum computer would also face - C. a Qiskit implementation detail - D. only true for single-qubit circuits

Question 10

$\langle Z \rangle$ computed from counts equals: - A. $P(0) + P(1)$ - B. $P(0) - P(1)$ - C. $P(0) \times P(1)$ - D. $P(1)$

Question 11

Estimating a full distribution over $n$ qubits to fixed precision costs shots growing like: - A. $n$ - B. $n^2$ - C. $2^n$ - D. constant

Question 12

Estimating a single expectation value to fixed precision costs shots growing like: - A. $2^n$ - B. $n$ - C. constant in $n$ - D. $n!$

Question 13

That difference is why which primitive exists? - A. Sampler - B. Estimator - C. AerSimulator - D. QiskitRuntimeService

Question 14

For the Bell state $|\Phi^+\rangle$, $\langle YY \rangle$ equals: - A. $+1$ - B. $-1$ - C. $0$ - D. $+0.5$

Question 15

For the Bell state, $\langle ZI \rangle$ equals: - A. $+1$ - B. $-1$ - C. exactly 0 - D. $+0.5$

Question 16

To measure in the $X$ basis, insert before measure: - A. x - B. h - C. s then h - D. nothing; it is automatic

Question 17

To measure in the $Y$ basis, insert: - A. y - B. h - C. sdg then h - D. h then s

Question 18

A marginal distribution is: - A. a quantum operation that collapses qubits - B. classical post-processing that sums over bits you already measured - C. a second experiment - D. only valid for product states

Question 19

A chi-squared test returns p = 0.55 for your data. You may conclude: - A. your circuit is correct - B. the data are consistent with your expectation, given the power of this experiment - C. your circuit is broken - D. you need fewer shots

Question 20

At 100 shots, a chi-squared test failed to detect a genuine 5-percentage-point bias. This is: - A. a bug in scipy - B. expected — the experiment lacked the statistical power to detect an effect that size - C. proof the bias does not exist - D. a sign the circuit is nondeterministic

Answers

# Answer Why
1 B The replacement is the part people forget, and it is irreversible. §5.1
2 B The basis is a parameter; the computational basis is a default, not a law. §5.1
3 B Certain in $X$, a fair coin in $Z$. §5.1, §5.6
4 A Rightmost character is qubit 0, and it is 0. §5.3
5 B The last-declared register appears leftmost. §5.3
6 C $\sqrt{p(1-p)/N} \le 1/(2\sqrt N)$, maximal at $p = 0.5$. §5.4
7 B Ten times the precision costs a hundred times the runs. §5.4
8 C $N \approx 0.96/\epsilon^2$. §5.4
9 B A perfect fault-tolerant machine faces it too. §5.4
10 B $+1$ for outcome 0, $-1$ for outcome 1. §5.5
11 C $2^n$ entries to estimate. §5.5
12 C One number, $O(1/\epsilon^2)$ shots, independent of $n$. §5.5
13 B Asking the right question is worth an exponential factor. §5.5
14 B Two factors of $i$ multiply to $-1$. §5.5 pitfall
15 C Each qubit alone carries no information. §5.5
16 B $HZH = X$. §5.6
17 C $S^\dagger$ rotates $Y$ onto $X$, then H onto $Z$. §5.6
18 B Free, and repeatable from one dataset. §5.7
19 B And the claim is empty without stating $N$ and the detectable effect size. §5.8
20 B A large p-value means low power, not correctness. §5.8

Topic Map

Questions Topic Section If you missed these
1, 2, 3 What measurement is §5.1 Reread §5.1; the "basis is a parameter" idea reframes everything after it
4, 5 Bitstrings and registers §5.3 Do Exercise 5.9 — the asymmetric-test lesson is the valuable part
6, 7, 8, 9 Sampling error §5.4 Run code/example-01-sampling-error.py. This governs every cost decision you will make
10, 11, 12, 13 Counts vs. expectation values §5.5 The exponential-factor argument is why Estimator exists
14, 15 Bell correlators §5.5 Exercise 5.13; the $\langle YY\rangle$ sign breaks real witnesses
16, 17 Basis rotations §5.6 Two gates; they finish Chapter 4's experiment
18 Marginals §5.7 Cheap, and easily confused with partial measurement
19, 20 Statistical power §5.8 The most misused idea in the chapter. Do Exercise 5.15

Score 16+: go to Chapter 6.

Score 12–15: if you lost points on 6–9, that cluster is the one to fix — the shot budget shapes every practical decision from here to Chapter 36. If you lost 19–20, reread §5.8's 🔬 Honest Assessment before you report any result to anyone.

Score under 12: the register-ordering details (4, 5) are reference. The three ideas to hold before Chapter 6 are: measurement replaces the state, precision costs $1/\epsilon^2$ shots, and an expectation value is one number rather than $2^n$.