Self-Assessment Quiz: The NISQ Era

Twenty questions on noisy intermediate-scale quantum computing: what NISQ means, error mitigation versus correction, and how to judge NISQ claims. Aim for 16+.

Question 1

NISQ, coined by Preskill in 2018, stands for:

A) Networked Ion-Scale Quantum B) Noisy Intermediate-Scale Quantum C) Non-Interacting Stabilizer Qubits D) Near-Ideal Superconducting Qubits

Question 2

The defining feature of a NISQ device is:

A) Fewer than 10 qubits B) Hundreds to thousands of qubits with no error correction C) Perfect gates D) Error-corrected logical qubits

Question 3

The usable circuit depth on a NISQ device is limited primarily by:

A) Memory B) Accumulated gate error and decoherence C) Classical compilation time D) Qubit count

Question 4

At a two-qubit gate error of $10^{-3}$, circuit fidelity falls to ~1/e after roughly:

A) 10 gates B) 100 gates C) 1,000 gates D) $10^6$ gates

Question 5

Error mitigation differs from error correction in that mitigation:

A) Removes errors from the quantum state B) Post-processes noisy results to estimate the noiseless value, without fixing the state C) Requires more qubits D) Is always exact

Question 6

Zero-noise extrapolation works by:

A) Deliberately amplifying noise, then extrapolating results back to zero noise B) Reducing gate count C) Adding ancilla qubits D) Measuring more often

Question 7

The cost of most error mitigation techniques is:

A) More qubits B) Exponentially more shots as circuit size grows C) Nothing D) Lower fidelity

Question 8

Probabilistic error cancellation requires:

A) A characterized noise model of the device B) No calibration C) Error correction D) Fewer shots

Question 9

NISQ algorithms are typically variational because:

A) Variational circuits are shallow, keeping depth within the coherence budget B) They are more accurate C) They need no measurement D) They avoid classical computers

Question 10

The classical optimizer in a variational algorithm:

A) Runs on the quantum device B) Runs classically, proposing new parameters from measured expectation values C) Is unnecessary D) Must be exact

Question 11

A "barren plateau" is:

A) A flat region of the cost landscape where gradients vanish exponentially with qubit count B) A hardware defect C) A type of error correction D) A measurement basis

Question 12

Which is not a recognized NISQ algorithm family?

A) VQE B) QAOA C) Shor's algorithm D) Quantum machine learning

Question 13

Preskill's own framing of NISQ was that it would:

A) Definitely deliver commercial advantage B) Be an interesting exploratory era whose usefulness was uncertain C) Replace classical computing D) Immediately break cryptography

Question 14

Quantum volume is a benchmark that:

A) Counts qubits only B) Combines qubit count, connectivity, and error rates into a single figure C) Measures runtime D) Is defined by qubit count squared

Question 15

A key criticism of quantum volume is:

A) It is too difficult to compute B) It saturates and can be gamed by optimizing for the specific benchmark circuits C) It ignores qubit count D) It requires error correction

Question 16

True or false: Error mitigation scales to arbitrarily large circuits.

Question 17

True or false: NISQ devices have demonstrated commercially valuable quantum advantage.

Question 18

True or false: Increasing shot count can compensate for arbitrarily deep noisy circuits.

Question 19

Short answer. Explain why error mitigation's shot overhead grows exponentially, and what that implies for NISQ scaling.

Question 20

Short answer. A vendor claims their 156-qubit device runs "1,000-gate circuits." What do you need to know before believing useful computation is possible?

Answer Key

Q Ans Note
1 B Preskill, "Quantum Computing in the NISQ era and beyond," 2018.
2 B Scale without correction is the defining tension: enough qubits to be classically hard, too noisy to be reliable.
3 B Both accumulate with depth; which binds depends on gate time versus $T_2$ (Ch. 7).
4 C $(1-10^{-3})^{1000} \approx 0.37$.
5 B Mitigation is statistical post-processing; the quantum state remains corrupted.
6 A Run at several amplified noise levels, fit, extrapolate to zero. Counter-intuitive but effective.
7 B The variance of the mitigated estimator grows exponentially with circuit size — the fundamental scaling barrier.
8 A PEC inverts a characterized noise channel by sampling, requiring accurate tomography of the noise.
9 A Depth is the scarce resource; variational circuits push work onto the classical optimizer.
10 B The hybrid loop: quantum evaluates, classical optimizes.
11 A Gradients vanish as $O(2^{-n})$, making the landscape untrainable for random deep ansätze.
12 C Shor needs error correction and depth far beyond NISQ.
13 B The original paper is notably cautious; the marketing that followed was not.
14 B A holistic benchmark — the largest square circuit the device can run successfully.
15 B Optimizing a device or compiler specifically for QV circuits inflates the score without improving general capability.
16 False Shot overhead grows exponentially with circuit volume, capping the practical reach — this is the hard limit on NISQ, not an engineering detail.
17 False No demonstration to date has shown commercially valuable advantage on a NISQ device. Supremacy experiments used contrived sampling tasks with no application.
18 False Shots reduce statistical error as $1/\sqrt N$ but do nothing about systematic corruption from decoherence. A circuit whose state has decohered returns a precise measurement of the wrong thing.
19 — Mitigation estimates the noiseless value from noisy runs; the estimator's variance grows with the amount of noise being undone, which grows with circuit volume. To hold the error bar fixed you need shots growing as roughly $e^{2\lambda}$ where $\lambda$ is total circuit error. So a modest depth increase can multiply the runtime by orders of magnitude. Implication: mitigation extends NISQ's reach by a constant-ish factor, and cannot substitute for error correction as circuits grow.
20 — Ask: (1) 1,000 gates of what — single- or two-qubit? Only the two-qubit count predicts fidelity. (2) What is the resulting circuit fidelity? At $10^{-3}$ two-qubit error, 1,000 two-qubit gates gives ~37%; at $7\times10^{-3}$ it gives $10^{-3}$. (3) Are those gates on the transpiled circuit including routing SWAPs? (4) Was the result verified against a classical simulation, and what error mitigation was applied at what shot cost? "Runs" usually means "executes without crashing," not "returns a correct answer."