Self-Assessment Quiz: The Capstone Portfolio

Twenty questions drawing together the eight portfolio projects and the practical skills the book has built. Aim for 16+.

Question 1

The Bell-state project verifies entanglement by:

A) Measuring correlations in multiple bases, not just the computational basis B) A computational-basis histogram alone C) Counting qubits D) Measuring one qubit

Question 2

Deutsch–Jozsa demonstrates:

A) An exponential query separation against deterministic classical algorithms B) Exponential separation against all classical algorithms C) A quadratic speedup D) No speedup

Question 3

Bernstein–Vazirani recovers the hidden string in:

A) One oracle query B) $n$ queries C) $2^n$ queries D) $\sqrt n$ queries

Question 4

The QFT project's output should be verified against:

A) A classical FFT of the amplitude vector B) Nothing C) Random data D) The input

Question 5

Grover's optimal iteration count for $N=16$, $M=1$ is:

A) 1 B) 3 C) 8 D) 16

Question 6

Running Grover past the optimum causes:

A) Success probability to decrease B) Saturation C) An error D) Faster convergence

Question 7

The simplified Shor project factors $N=15$ using:

A) Period finding on $a^x \bmod 15$ plus classical post-processing B) Trial division C) Grover search D) Annealing

Question 8

The continued-fraction step converts:

A) The measured value into a candidate period B) The period into factors C) Bits into qubits D) Nothing

Question 9

VQE on H₂ produces:

A) A variational upper bound on the ground-state energy B) The exact energy always C) A lower bound D) A time evolution

Question 10

If a VQE energy falls below the known exact value, it indicates:

A) Uncorrected systematic error — the variational bound has been violated B) Success C) A better ansatz D) Nothing unusual

Question 11

QAOA on MaxCut returns:

A) Samples, from which you take the best cut found B) The guaranteed optimum C) An exact solution D) A single deterministic answer

Question 12

Across the portfolio, the observable most sensitive to hardware noise is:

A) Deep-circuit outputs such as Shor's period finding B) Single-qubit measurements C) Bell-state parity D) Classical post-processing

Question 13

Comparing hardware against a noiseless simulator is:

A) The wrong baseline — use a noise model built from the device's properties B) The correct baseline C) Unnecessary D) Impossible

Question 14

Every portfolio result should report:

A) Raw counts, shot count, backend, and calibration timestamp B) Only the final answer C) Only the mitigated value D) Only accuracy

Question 15

The portfolio's projects are all classically simulable. That is:

A) Intentional — it allows exact verification of each result B) A flaw C) Accidental D) A limitation of Qiskit

Question 16

True or false: Successfully running these projects demonstrates quantum advantage.

Question 17

True or false: Error mitigation should be applied before reporting raw counts.

Question 18

True or false: The same circuit on the same backend gives identical results across days.

Question 19

Short answer. Why should every portfolio project be verified against a classical computation?

Question 20

Short answer. What is the single most important habit the portfolio is meant to instill?

Answer Key

Q Ans Note
1 A A computational-basis histogram is reproducible by a classical coin flip (Ch. 5).
2 A The separation is against deterministic classical algorithms; randomized ones need only a few queries (Ch. 12).
3 A One query, deterministically.
4 A The QFT's amplitudes are the discrete Fourier transform of the input's.
5 B $\lfloor\frac{\pi}{4}\sqrt{16}\rfloor = \lfloor 3.14\rfloor = 3$.
6 A Over-rotation — the state rotates past the target (Ch. 13).
7 A The quantum part finds the period; everything else is classical number theory.
8 A Continued fractions on $y/2^t$ yield a denominator that is a period candidate.
9 A The Rayleigh–Ritz bound, valid only if the measurement is unbiased.
10 A Noise breaks the variational guarantee — a valuable self-check (Ch. 19).
11 A It is a heuristic sampler, not an exact solver.
12 A Depth drives error accumulation; Shor's is by far the deepest project here.
13 A Match against the backend's own noise model and treat agreement as success (Ch. 8).
14 A Raw counts are the primary datum; everything else is derived (Ch. 8).
15 A You cannot learn to verify results on problems you cannot verify.
16 False Every project is classically trivial. They demonstrate that you can implement, run, and verify quantum algorithms — a different and prerequisite skill.
17 False Report raw counts always, with mitigated values alongside and the method stated. Mitigated-only reporting is unauditable.
18 False Calibration drifts, TLS defects move, and devices are recalibrated. Record the calibration timestamp with every result (Ch. 26).
19 — Because a quantum computer returns a plausible-looking distribution whether or not the circuit is correct. Without a classical reference you cannot distinguish a working implementation from a broken one producing noise, an endianness error, or a mis-transpiled circuit. Verification at small scale is the only way to build justified confidence in an implementation before applying it where verification is impossible — which is the entire point of eventually running quantum algorithms.
20 — Verify everything, and report honestly. Concretely: compare against the correct classical baseline, check against a noise model rather than an ideal simulator, publish raw counts with backend and timestamp, separate statistical from systematic error, and state precisely what was and was not demonstrated. The algorithms in this portfolio will be superseded; the habit of disciplined verification is what transfers.