IBM C1000-179 — Fundamentals of Quantum Computing Using Qiskit v2.X Developer Passing target: 24/34. All code outputs were verified with qiskit 2.5.1 / qiskit-ibm-runtime 0.48.0.

Answer Key

Q	Ans	Q	Ans	Q	Ans	Q	Ans
1	B	10	A	19	C	28	B
2	C	11	A	20	A	29	B
3	A	12	C	21	D	30	A
4	C	13	B	22	B	31	A
5	B	14	A	23	A	32	B
6	D	15	C	24	C	33	B
7	A	16	B	25	B	34	C
8	B	17	A	26	D
9	B	18	A, C	27	A

Explanations

Q1 — B (3). Depth is the longest path of gate layers: h(0) is layer 0, cx(0,1) layer 1, cx(1,2) layer 2. The x(0) also fits in layer 2 because qubit 0 is idle there. Distractors: C (4) is the trap for counting x(0) as a fourth sequential layer; A (2) forgets the second CX must wait for the first; D counts every instruction.

Q2 — C (4 4). size() counts instructions: h + cx + 2 measure = 4. width() counts qubits plus clbits: 2 + 2 = 4. A common mistake is thinking width() is qubits only (options A/B).

Q4 — C. measure_all() adds a barrier and a fresh ClassicalRegister named 'meas' sized to the qubit count, then measures every qubit. It never requires a pre-existing register.

Q5 — B (1). qc.parameters is a set-like view of unique Parameter objects. The same theta used in two gates counts once. Reuse is perfectly legal (D is false).

Q6 — D. generate_preset_pass_manager takes optimization_level 0–3; 3 is the heaviest. Its output pass manager fully transpiles the circuit — no extra transpile() call is needed (C is a V1-era habit).

Q7 — A ({'01': 1.0}). Little-endian: x(0) flips qubit 0, and qubit 0 is the rightmost character of the bitstring, so the state label is '01'. Distractor B ('10') is the classic big-endian misreading. Verified by execution.

Q8 — B. simplify() merges the two XX terms (1.0 + 2.0 = 3.0) and drops the zero-coefficient ZZ term, leaving SparsePauliOp(['XX'], coeffs=[3.+0.j]). C forgets that zero terms are removed; duplicates are allowed before simplification (D false).

Q9 — B (|1⟩). This is the identity HZH = X: applied to |0⟩ it yields |1⟩ (probability of '1' is 1.0 up to ~1e-16 float noise). Distractors: A is what you get if you think the H's simply cancel; D (|−⟩) is the state after H·Z but before the final H. Verified by execution.

Q10 — A. H then CX is the entangler. B and C produce product states; D leaves a single qubit in |−⟩ — one qubit can never be entangled with nothing.

Q11 — A (1.0). |+⟩ is the +1 eigenstate of X, so ⟨+|X|+⟩ = 1. B (0.0) would be ⟨+|Z|+⟩. Verified by execution.

Q12 — C. Z flips the sign of the |1⟩ component: Z|+⟩ = |−⟩. X leaves |+⟩ unchanged, H maps |+⟩→|0⟩, S maps |+⟩→|i⟩.

Q13 — B. Iterative, feedback-driven workloads (VQE) are exactly what Session mode's dedicated access window is for. Batch is for independent jobs; job mode re-queues every request.

Q14 — A. service.least_busy(operational=True, simulator=False) is the v2.x API. D is the old provider-era least_busy() helper function.

Q15 — C. V2 primitives on IBM hardware only accept ISA circuits — already transpiled to the backend's basis gates and coupling map. The service does not auto-transpile (A is the pre-primitives behavior people remember); the job is rejected with an error, it never runs (B, D).

Q16 — B. The Qiskit patterns flow: build → generate_preset_pass_manager → pm.run(qc) → SamplerV2(mode=backend).run([isa]). A uses qiskit.execute, removed in Qiskit 1.0. C (backend.run) is the deprecated V1 path. D is V1 Sampler syntax.

Q17 — A. qiskit.primitives.StatevectorSampler implements the same V2 PUB/result interface with ideal statevector simulation, no account needed. There is no channel="local" service for this purpose (B), and C/D are V1 patterns.

Q18 — A and C. Sampler circuits must contain measurements, and the result exposes per-shot data (BitArray → get_counts(), get_bitstrings()). B describes the Estimator; D never happens — a measurement-free circuit is an error.

Q19 — C ({'01': 1000}). x(0) sets qubit 0 to 1; little-endian puts it rightmost: '01', deterministically for all 1000 shots. Distractors: A is the big-endian trap; B invents randomness where there is none; D forgets measure_all() measures both qubits, so bitstrings have 2 bits. Verified by execution.

Q20 — A. The classical register created by QuantumCircuit(2, 2) is named 'c', and V2 sampler data is keyed by register name: result[0].data.c. Distractors: B (.data.meas) only exists when measure_all() created the 'meas' register; C is the old Result.get_counts API; D (quasi_dists) is the V1 Sampler result format. Verified by execution.

Q21 — D. resilience_level is an Estimator-only option — Sampler output is raw samples, so there is no expectation-value mitigation to configure. Shots, dynamical decoupling, and twirling (A–C) are all valid Sampler options.

Q22 — B. The Estimator computes ⟨ψ|O|ψ⟩ analytically from the pre-measurement state; measurement instructions in the circuit are an error, not ignored.

Q23 — A ([0. 1.]). For H|0⟩ = |+⟩: ⟨Z⟩ = 0 and ⟨X⟩ = 1, in the order the observables were listed. Distractors: B swaps the order; D is the Sampler rule (measurements required) misapplied — Estimator circuits must NOT have measurements. Verified by execution: prints [0. 1.].

Q24 — C. Transpilation may move logical qubits to different physical qubits; obs.apply_layout(isa_circuit.layout) re-expresses the observable on the physical qubits. Forgetting this is a top exam trap — nothing remaps the observable for you (A), and observables are not circuits so they cannot be transpiled or composed (B, D).

Q25 — B. Level 0 = no mitigation; level 1 (default) = measurement/readout mitigation (TREX); level 2 = level 1 + ZNE. PEC is opt-in, not a default level (C).

Q26 — D. Individually, each qubit of a Bell pair is maximally mixed, so its Bloch vector has zero length — both arrows sit at the sphere centers. This is the standard visual signature of entanglement in plot_bloch_multivector.

Q27 — A. Top wire is q0 (H then the control dot ■); bottom wire q1 carries the ⊕/X target, so the code is h(0); cx(0, 1) — control 0, target 1. Drawing verified by execution.

Q28 — B. On the qsphere, blob size encodes amplitude magnitude/probability, and color encodes phase.

Q29 — B. |+⟩/|−⟩ are the ±X eigenstates, |±i⟩ the ±Y ones, |0⟩/|1⟩ the ±Z ones. So |−⟩ points along −X.

Q30 — A. Runtime jobs persist on the service; QiskitRuntimeService().job(job_id) retrieves them from any session. C is the old backend/provider API.

Q31 — A (0.2). ⟨Z⟩ = (n₀ − n₁)/shots = (600 − 400)/1000 = 0.2. B flips the sign convention (|0⟩ has Z-eigenvalue +1).

Q32 — B (4,000). Standard error scales as 1/√shots; halving the error requires 4× the shots.

Q33 — B ({'10': 100}). x q[1] sets qubit 1, and qubit 1 is the left character of a 2-bit little-endian string: '10'. Distractor A ('01') is the big-endian misread of the QASM index. Verified by execution.

Q34 — C. qiskit.qasm3.dumps(qc) returns the program as a string; dump (B) writes to a file object. qc.qasm() (A) was the QASM 2 exporter removed in Qiskit 1.0; D does not exist.