Sample Papers

Paper 10 (full length)

Exam: IBM C1000-179 — Fundamentals of Quantum Computing Using Qiskit v2.X Developer Questions: 68 (single best answer unless marked "choose two") Time limit: 90 minutes (~79 seconds per question) Passing score: 47 / 68 (≈69%)

Rules for the rehearsal: closed book, no interpreter, no pausing the clock. Mark uncertain questions and return to them; an unanswered question is always wrong. All code assumes Qiskit v2.x with qiskit-ibm-runtime (V2 primitives) and the standard imports shown in each snippet. Bitstrings are little-endian: qubit 0 is the rightmost character.

Section 1 — Create Quantum Circuits (Q1–Q12)

Q1. A researcher benchmarks circuit metrics before submitting to hardware:

from qiskit import QuantumCircuit
qc = QuantumCircuit(3)
qc.h(0)
qc.cx(0, 1)
qc.cx(1, 2)
qc.barrier()
qc.measure_all()
print(qc.depth())

What is printed?

A. 3
B. 4
C. 5
D. 6

Q2. Two engineers build fragments of a workflow:

from qiskit import QuantumCircuit
a = QuantumCircuit(2)
a.h(0); a.cx(0, 1)
b = QuantumCircuit(2)
b.cx(0, 1); b.h(0)
c = a.compose(b.inverse())
print(dict(c.count_ops()), c.depth())

What is printed?

A. {} 0 — the circuits cancel to the identity
B. {'h': 2, 'cx': 2} 2
C. {'h': 2, 'cx': 2} 4
D. {'h': 1, 'cx': 1} 2

Q3. A researcher needs the singlet Bell state |Ψ⁻⟩ = (|01⟩ − |10⟩)/√2 as the input to an entanglement test. Starting from |00⟩, which snippet prepares it?

A. qc.h(0); qc.cx(0, 1)
B. qc.h(0); qc.cx(0, 1); qc.x(1)
C. qc.h(0); qc.cx(0, 1); qc.z(0)
D. qc.h(0); qc.cx(0, 1); qc.x(1); qc.z(1)

Q4. A student binds parameters by position and then samples the circuit with 1000 shots on an ideal simulator:

import numpy as np
from qiskit import QuantumCircuit
from qiskit.circuit import Parameter
 
phi, theta = Parameter('phi'), Parameter('theta')
qc = QuantumCircuit(1)
qc.rx(theta, 0)
qc.rz(phi, 0)
bound = qc.assign_parameters([np.pi, np.pi / 2])

Which measurement distribution (in the Z basis) results?

A. Approximately 50% '0' and 50% '1'
B. 100% '1'
C. 100% '0'
D. Approximately 85% '0' and 15% '1'

Q5. Which diagram is produced by qc.draw('text')?

qc = QuantumCircuit(3)
qc.h(0)
qc.cx(0, 2)
qc.x(1)
qc.cz(1, 2)

     ┌───┐┌───┐
q_0: ┤ H ├┤ X ├───
     ├───┤└─┬─┘
q_1: ┤ X ├──┼───■─
     └───┘  │   │
q_2: ───────■───■─

     ┌───┐
q_0: ┤ H ├──■─────
     ├───┤  │
q_1: ┤ X ├──┼───■─
     └───┘┌─┴─┐ │
q_2: ─────┤ X ├─■─
          └───┘

     ┌───┐
q_0: ┤ H ├──■──────────
     └───┘┌─┴─┐┌───┐
q_1: ─────┤ X ├┤ X ├─■─
          └───┘└───┘ │
q_2: ────────────────■─

     ┌───┐
q_0: ┤ H ├──■────■──
     └───┘  │    │
q_1: ───────┼────■──
          ┌─┴─┐┌───┐
q_2: ─────┤ X ├┤ X ├
          └───┘└───┘

Q6. After a mid-circuit measurement into classical register cr, a researcher wants to apply X if cr reads 1 and Z otherwise (classical feedforward). Which snippet is correct in Qiskit v2.x?

A. qc.x(0).c_if(cr, 1); qc.z(0).c_if(cr, 0)
B. if qc.measure(0, 0) == 1: qc.x(0) else: qc.z(0)
C.

with qc.if_test((cr, 1)) as else_:
    qc.x(0)
with else_:
    qc.z(0)

qc.if_test((cr, 1), qc.x(0), qc.z(0))

Q7. A 2-qubit Bell fragment is stitched into a larger register:

base = QuantumCircuit(3)
sub = QuantumCircuit(2)
sub.h(0); sub.cx(0, 1)
out = base.compose(sub, qubits=[2, 0])

Which statement describes out?

A. H acts on qubit 2; the CNOT has control qubit 2 and target qubit 0
B. H acts on qubit 0; the CNOT has control qubit 0 and target qubit 2
C. H acts on qubit 2; the CNOT has control qubit 0 and target qubit 2
D. compose raises an error because sub has fewer qubits than base

Q8. A lab implements standard teleportation of qubit 0's state to qubit 2. After the Bell measurement of qubits 0 and 1 into classical bits c0 and c1, which correction must be applied to qubit 2?

A. X conditioned on c0, then Z conditioned on c1 — but only if both bits are 1
B. H conditioned on c0 and S conditioned on c1
C. Z conditioned on both bits jointly equal to 0b11
D. X on qubit 2 conditioned on the measurement of qubit 1, and Z on qubit 2 conditioned on the measurement of qubit 0

Q9. A single Hadamard is translated for a heavy-hex device:

qc = QuantumCircuit(1)
qc.h(0)
pm = generate_preset_pass_manager(optimization_level=1,
                                  basis_gates=['rz', 'sx', 'x', 'cx'])
print(dict(pm.run(qc).count_ops()))

What is printed?

A. {'u': 1}
B. {'rz': 2, 'sx': 1}
C. {'rz': 1, 'sx': 2}
D. {'x': 1, 'sx': 1}

Q10. Which statement about generate_preset_pass_manager optimization levels in Qiskit v2.x is TRUE?

A. Level 0 skips layout and routing entirely, so the output may not match the coupling map
B. Level 3 is the default when optimization_level is omitted
C. Higher levels apply progressively more aggressive circuit optimization and typically take longer to compile
D. Level 1 automatically enables zero-noise extrapolation

Q11. What does qc.width() return here?

from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.circuit import AncillaRegister
qr = QuantumRegister(3, 'q')
anc = AncillaRegister(2, 'a')
cr = ClassicalRegister(3, 'c')
qc = QuantumCircuit(qr, anc, cr)

A. 3
B. 5
C. 6
D. 8

Q12. A researcher squares a phase gate:

from qiskit.quantum_info import Operator
qs = QuantumCircuit(1); qs.s(0)
zc = QuantumCircuit(1); zc.z(0)
print(Operator(qs.power(2)).equiv(Operator(zc)))

What is printed?

A. True
B. False, because power only accepts parameterized circuits
C. False, because S² = T
D. True only if qs.power(2) is transpiled first

Section 2 — Perform Quantum Operations (Q13–Q23)

Q13. A researcher constructs Pauli('XZ') for a 2-qubit experiment. Which single-qubit operator acts on qubit 0?

A. X, because the string is read left to right starting at qubit 0
B. Z, because Pauli strings are little-endian: the rightmost character acts on qubit 0
C. Both act on qubit 0; Pauli('XZ') is the product XZ on one qubit
D. Neither — 'XZ' is an invalid Pauli label

Q14. What does this print?

from qiskit.quantum_info import SparsePauliOp
op = SparsePauliOp.from_list([("XZ", 1.0), ("XZ", 1.0),
                              ("II", 2.0), ("YY", 0.0)])
print(op.simplify())

A. SparsePauliOp(['XZ', 'XZ', 'II', 'YY'], coeffs=[1, 1, 2, 0])
B. SparsePauliOp(['XZ', 'II', 'YY'], coeffs=[2, 2, 0])
C. SparsePauliOp(['XZ', 'II'], coeffs=[2.+0.j, 2.+0.j])
D. SparsePauliOp(['II'], coeffs=[4.+0.j])

Q15. What is Statevector.from_label('01').data?

A. [0, 0, 1, 0] — the amplitude sits at index 2
B. [0, 1, 0, 0] — the amplitude sits at index 1
C. [1, 0, 0, 0]
D. [0, 0, 0, 1]

Q16. A state is evolved through a small circuit:

sv = Statevector.from_label('00')
qc = QuantumCircuit(2)
qc.h(0); qc.cx(0, 1); qc.x(1)
print(sv.evolve(qc).probabilities_dict())

What is printed (up to float rounding)?

A. {'00': 0.5, '11': 0.5}
B. {'00': 1.0}
C. {'11': 1.0}
D. {'01': 0.5, '10': 0.5}

Q17. During a debugging session, a colleague wraps a Z gate between two Hadamards on the same qubit: qc.h(0); qc.z(0); qc.h(0). This sequence is equivalent to which single gate?

A. X
B. Z
C. Y
D. S

Q18. For the Bell state prepared by h(0); cx(0, 1), what does the following print?

sv = Statevector.from_instruction(bell)
print(sv.expectation_value(Pauli('ZZ')),
      sv.expectation_value(Pauli('XX')),
      sv.expectation_value(Pauli('ZI')))

A. 1.0 0.0 1.0
B. 0.0 0.0 0.0
C. 1.0 1.0 0.0
D. 1.0 -1.0 0.5

Q19. A researcher checks whether an RZ rotation reproduces a Z gate:

qrz = QuantumCircuit(1); qrz.rz(np.pi, 0)
zc = QuantumCircuit(1); zc.z(0)
print(Operator(qrz).equiv(Operator(zc)), Operator(qrz) == Operator(zc))

What is printed?

A. True True
B. True False
C. False False
D. False True

Q20. For a 4-qubit device study, an observable applying Z only to qubit 2 (identity elsewhere) is needed. Which construction is correct?

A. SparsePauliOp.from_sparse_list([("Z", [2], 1.0)], num_qubits=4)
B. SparsePauliOp.from_list([("ZIII", 1.0)])
C. SparsePauliOp.from_list([("IIZI", 1.0)], num_qubits=4) — from_list requires num_qubits
D. Pauli("Z", qubit=2)

Q21. What does this print?

from qiskit.quantum_info import Pauli
print(Pauli('X').tensor(Pauli('Z')), Pauli('X').expand(Pauli('Z')))

A. ZX XZ
B. XZ XZ
C. ZX ZX
D. XZ ZX

Q22. What does state_fidelity(Statevector.from_label('+'), Statevector.from_label('0')) return?

A. 0.7071
B. 0.5
C. 0.25
D. 1.0

Q23. (Choose two.) Which of the following operator pairs commute?

A. Pauli('X') and Pauli('Z')
B. Pauli('XX') and Pauli('ZZ')
C. Pauli('Z') and an rz(0.7) rotation on the same qubit
D. Pauli('X') and Pauli('Y')

Section 3 — Run Quantum Circuits (Q24–Q33)

Q24. A researcher wants the real device with the shortest queue that is currently online. Which call is correct?

A. service.least_busy(operational=True, simulator=False)
B. service.backends(least_busy=True, real=True)
C. service.get_backend("least_busy")
D. service.least_busy(queue="shortest")

Q25. A circuit containing an h gate (not in the backend's basis) and no layout is submitted directly to SamplerV2(mode=backend) for an IBM hardware backend. What happens?

A. The server transpiles it automatically before execution
B. It runs, but a warning about reduced fidelity is logged
C. The job is rejected with an error because the circuit is not an ISA circuit
D. The unsupported gates are silently skipped

Q26. A variational-algorithm loop needs dozens of sequential Estimator calls where each iteration depends on the previous result, without re-queuing between iterations. Which pattern is the intended one?

A. estimator = EstimatorV2(mode=Batch(backend=backend))
B.

with Session(backend=backend) as session:
    estimator = EstimatorV2(mode=session)
    # iterate: run, read result, update parameters

C. estimator = EstimatorV2(mode=backend) called in a Python for loop
D. session = backend.open_session(); estimator.run(session)

Q27. A group has 500 fully independent circuits (no feedback between jobs) and wants them scheduled efficiently as a single workload. Which execution mode fits best?

A. Session mode, because it reserves the device
B. Job mode, one submission per circuit
C. Local StatevectorSampler, since 500 circuits never run on hardware
D. Batch mode, which groups independent jobs for parallel scheduling

Q28. Which snippet runs a single ISA circuit in job mode on a specific backend object?

A. sampler = SamplerV2(mode=backend); job = sampler.run([isa_circuit])
B. job = backend.run(isa_circuit, primitive="sampler")
C. sampler = SamplerV2(backend.name); job = sampler.run(isa_circuit)
D. job = execute(isa_circuit, backend, shots=1024)

Q29. A GHZ circuit h(0); cx(0,1); cx(0,2); measure_all() is run with StatevectorSampler for 1000 shots. Which counts dictionary is plausible?

A. {'000': 250, '001': 250, '110': 250, '111': 250}
B. {'000': 1000}
C. {'111': 497, '000': 503}
D. {'100': 340, '010': 330, '001': 330}

Q30. What is printed?

qc = QuantumCircuit(1, 1); qc.h(0); qc.measure(0, 0)
result = StatevectorSampler(seed=1).run(
    [(qc, None, 2048), (qc,)], shots=1024).result()
print(result[0].data.c.num_shots, result[1].data.c.num_shots)

A. 1024 1024 — the run-level shots always wins
B. 2048 1024 — a PUB-level shot count overrides the run-level value
C. 2048 2048 — the first PUB sets shots for the whole job
D. A ValueError, because shots may only be set in one place

Q31. Why would a developer use FakeManilaV2 from qiskit_ibm_runtime.fake_provider during development?

A. It forwards jobs to the real Manila device at reduced cost
B. It is a 127-qubit noiseless statevector simulator
C. It validates OpenQASM syntax without executing anything
D. It runs locally with a noise model and coupling map snapshotted from the real device, so ISA transpilation and primitive workflows can be tested without queueing

Q32. Review this workflow destined for real hardware:

qc = QuantumCircuit(2)
qc.h(0); qc.cx(0, 1)
qc.measure_all()
pm = generate_preset_pass_manager(optimization_level=2, backend=backend)
isa = pm.run(qc)
sampler = SamplerV2(mode=backend)
job = sampler.run([qc])

What is the outcome?

A. It works: pm.run modifies qc in place
B. It works, but with more noise than necessary
C. The job fails: the untranspiled qc was submitted instead of isa, so the circuit does not match the backend ISA
D. pm.run raises an error because the circuit contains measurements

Q33. Which snippet correctly saves IBM Quantum Platform credentials for later QiskitRuntimeService() calls?

A. QiskitRuntimeService.save_account(channel="ibm_quantum_platform", token=MY_TOKEN, set_as_default=True)
B. QiskitRuntimeService.save_account(channel="ibm_quantum", token=MY_TOKEN)
C. QiskitRuntimeService(api_key=MY_TOKEN).save()
D. IBMQ.save_account(MY_TOKEN)

Section 4 — Use the Sampler Primitive (Q34–Q41)

Q34. A researcher runs the following and hits a problem:

qc = QuantumCircuit(2, 2)
qc.x(0)
qc.measure([0, 1], [0, 1])
result = sampler.run([qc]).result()
print(result[0].data.meas.get_counts())

What happens?

A. {'01': 1024} is printed
B. An AttributeError: the classical register is named c, so the data field is result[0].data.c; .meas exists only when measure_all() created the register
C. {'10': 1024} is printed
D. An error: SamplerV2 requires measure_all() rather than explicit measure

Q35. A 2-qubit circuit applies x(1) then measure_all() and is sampled for 100 shots on an ideal simulator. What is get_counts()?

A. {'01': 100}
B. {'11': 100}
C. {'10': 100}
D. {'1': 100}

Q36. A student passes a circuit with no measurement instructions to StatevectorSampler. What is the behavior?

A. The sampler measures all qubits implicitly, like measure_all()
B. A hard error is always raised before the job starts
C. It returns the exact statevector instead of samples
D. A warning is emitted and the PUB result's DataBin is empty — there is no classical output to sample

Q37. What is get_counts() after this parameterized run (200 shots, ideal)?

th = Parameter('th')
qc = QuantumCircuit(1, 1)
qc.ry(th, 0)
qc.measure(0, 0)
job = sampler.run([(qc, [np.pi])], shots=200)

A. {'1': 200}
B. {'0': 200}
C. {'0': 100, '1': 100}
D. An error: parameter values must be a dict

Q38. A device suffers decoherence on idle qubits during long circuits. Which snippet enables the appropriate suppression technique on a Sampler?

A. sampler.options.resilience_level = 2
B.

sampler.options.dynamical_decoupling.enable = True
sampler.options.dynamical_decoupling.sequence_type = "XpXm"

C. sampler.options.zne_mitigation = True
D. sampler.options.default_shots = 100_000

Q39. A teammate copies Estimator configuration onto a Sampler: sampler.options.resilience_level = 1. What is the correct assessment?

A. Valid — level 1 enables TREX on the Sampler
B. Valid but ignored silently
C. Invalid — resilience_level is an Estimator option; SamplerV2 supports twirling, dynamical decoupling, and shot options instead
D. Invalid — Sampler options are read-only after instantiation

Q40. A circuit measures qubit 0 (after an X gate) into 1-bit register first and qubit 1 into 1-bit register second. With 50 ideal shots:

print(result[0].join_data().get_counts())

What is printed?

A. {'10': 50}
B. {'1 0': 50}
C. {'11': 50}
D. {'01': 50} — registers are concatenated with later-added registers as the more significant bits

Q41. A 2-qubit measure_all() circuit is sampled with shots=100. For ba = result[0].data.meas, what is (ba.num_shots, ba.num_bits, len(ba.get_bitstrings()))?

A. (100, 2, 100)
B. (100, 2, 4)
C. (2, 100, 100)
D. (100, 4, 100)

Section 5 — Use the Estimator Primitive (Q42–Q49)

Q42. For the Bell state circuit (no measurements), what does this print?

est = StatevectorEstimator()
obs = [SparsePauliOp('ZZ'), SparsePauliOp('XX'), SparsePauliOp('ZI')]
result = est.run([(bell, obs)]).result()
print(result[0].data.evs)

A. [0. 0. 0.]
B. [1. 1. 0.]
C. [1. 0. 1.]
D. [0.5 0.5 0.5]

Q43. A researcher reuses a Sampler circuit (ending in measure_all()) in an Estimator PUB with observable ZZ. What happens?

A. The measurements are ignored and ⟨ZZ⟩ is returned
B. The estimator converts the measurements into the observable basis
C. An error is raised — Estimator circuits must not contain measurements; the observable defines the measurement basis
D. evs is returned, but doubled because measurement and observable overlap

Q44. Which snippet is the correct end-to-end hardware Estimator workflow for a Bell circuit and observable ZZ?

pm = generate_preset_pass_manager(optimization_level=1, backend=backend)
isa = pm.run(bell)
mapped = SparsePauliOp('ZZ').apply_layout(isa.layout)
estimator = EstimatorV2(mode=backend)
ev = estimator.run([(isa, mapped)]).result()[0].data.evs

isa = pm.run(bell)
estimator = EstimatorV2(mode=backend)
ev = estimator.run([(isa, SparsePauliOp('ZZ'))]).result()[0].data.evs

mapped = SparsePauliOp('ZZ').apply_layout(bell.layout)
isa = pm.run(bell)
ev = estimator.run([(isa, mapped)]).result()[0].data.evs

isa = pm.run(bell)
mapped = isa.apply_layout(SparsePauliOp('ZZ'))
ev = estimator.run([(isa, mapped)]).result()[0].data.evs

Q45. A parameter sweep uses broadcasting:

t = Parameter('t')
qc = QuantumCircuit(1); qc.rx(t, 0)
obs = [[SparsePauliOp('Z')], [SparsePauliOp('X')]]     # shape (2, 1)
params = [[0.0], [np.pi / 2], [np.pi]]                 # 3 parameter sets
result = StatevectorEstimator().run([(qc, obs, params)]).result()
print(result[0].data.evs.shape)
print(np.round(result[0].data.evs, 3))

What is printed?

A. (3,) then [1. 0. -1.]
B. (6,) then [1. 0. -1. 0. 0. 0.]
C. An error — observables and parameter sets must have identical shapes
D. (2, 3) then [[ 1. 0. -1.] [ 0. 0. 0.]]

Q46. Which statement about Runtime Estimator resilience levels is TRUE?

A. Level 0 applies measurement-error mitigation only
B. Level 1 (the default) applies measurement-error mitigation (TREX); level 2 adds zero-noise extrapolation
C. Level 2 applies probabilistic error cancellation by default
D. Level 1 disables all twirling

Q47. A researcher wants explicit ZNE with noise factors 1, 3, 5 and an exponential extrapolator. Which configuration is correct?

A. estimator.options.zne = {"factors": [1, 3, 5], "fit": "exp"}
B. estimator.options.resilience_level = 3
C.

estimator.options.resilience.zne_mitigation = True
estimator.options.resilience.zne.noise_factors = (1, 3, 5)
estimator.options.resilience.zne.extrapolator = "exponential"

D. estimator.options.dynamical_decoupling.enable = True with sequence_type="ZNE"

Q48. For qc.rx(np.pi/3, 0) on one qubit, what does the Estimator return for observable Z (ideal)?

A. 0.5
B. 0.866
C. -0.5
D. 1.0

Q49. (Choose two.) A paper's methods section must separate error suppression from error mitigation. Which two techniques are suppression (acting before/during execution rather than in post-processing)?

A. Dynamical decoupling
B. Zero-noise extrapolation
C. Pauli twirling
D. Probabilistic error cancellation

Section 6 — Visualize Circuits, Measurements, and States (Q50–Q57)

Q50. Which code produces this draw('text') output?

     ┌───┐┌───┐     ┌─┐
q_0: ┤ H ├┤ Z ├──■──┤M├───
     └───┘└───┘┌─┴─┐└╥┘┌─┐
q_1: ──────────┤ X ├─╫─┤M├
               └───┘ ║ └╥┘
c: 2/════════════════╩══╩═
                     0  1

A. qc.z(0); qc.h(0); qc.cx(0, 1); qc.measure([0, 1], [0, 1])
B. qc.h(0); qc.z(0); qc.cx(0, 1); qc.measure([0, 1], [0, 1])
C. qc.h(0); qc.z(1); qc.cx(0, 1); qc.measure([0, 1], [0, 1])
D. qc.h(0); qc.z(0); qc.cx(1, 0); qc.measure([0, 1], [0, 1])

Q51. A textbook draws its circuits with the most significant qubit on top, but draw() puts q_0 on top by default. Which call matches the textbook layout?

A. qc.draw('mpl', flip=True)
B. qc.draw('text', idle_wires=False)
C. qc.draw('mpl', reverse_bits=True)
D. qc.reverse_bits_draw()

Q52. plot_bloch_multivector is called on the Bell state (|00⟩ + |11⟩)/√2. What does the figure show?

A. Both per-qubit Bloch vectors have zero length (points at the sphere's center) because each reduced state is maximally mixed
B. Both vectors point along +X
C. Qubit 0 along +Z, qubit 1 along −Z
D. One combined sphere with two arrows at ±Z

Q53. On a plot_state_qsphere figure, how are amplitude and phase encoded?

A. Amplitude = color, phase = distance from the pole
B. Amplitude = arrow direction, phase = arrow length
C. Both are encoded as latitude on the sphere
D. The blob size reflects the probability of the basis state; the color encodes its relative phase

Q54. A 3-qubit circuit applies only x(2) then measure_all(); the counts are passed to plot_histogram. What does the plot show?

A. A single bar at '001'
B. A single bar at '100'
C. Two bars at '000' and '100'
D. Eight equal bars

Q55. A researcher wants ideal-simulator counts and hardware counts on one histogram, labeled. Which call is correct?

A. plot_histogram([ideal_counts, hw_counts], legend=["ideal", "hardware"])
B. plot_histogram(ideal_counts + hw_counts, labels=["ideal", "hardware"])
C. plot_histogram({"ideal": ideal_counts, "hardware": hw_counts})
D. plot_histogram(ideal_counts, overlay=hw_counts)

Q56. The state (|0⟩ − i|1⟩)/√2 sits where on the Bloch sphere?

A. +Y axis
B. −X axis
C. −Y axis
D. +Z axis

Q57. A single qubit undergoes h(0) then s(0), and plot_bloch_multivector is called on the resulting statevector. Where does the vector point?

A. +X axis — S leaves |+⟩ unchanged
B. −Z axis
C. −Y axis
D. +Y axis — the state is (|0⟩ + i|1⟩)/√2

Section 7 — Retrieve and Analyze Results (Q58–Q64)

Q58. A job was submitted yesterday from a laptop that has since been rebooted; only the job ID string was saved. How is the result retrieved?

A. job = SamplerV2.retrieve(job_id); job.result()
B. service = QiskitRuntimeService(); job = service.job(job_id); result = job.result()
C. result = backend.results(job_id)
D. Results are lost when the Python session ends

Q59. Hardware counts for a 1-qubit circuit are {'0': 600, '1': 400} (1000 shots). What is the estimate of ⟨Z⟩ computed from these counts?

A. 0.2
B. 0.6
C. -0.2
D. 0.4

Q60. An Estimator result's standard error is twice as large as the target. Approximately how must the shot count change to halve the standard error?

A. Double the shots
B. Halve the shots
C. Quadruple the shots — standard error scales as 1/√shots
D. Increase shots by √2

Q61. Three Sampler PUBs are submitted in one run call. What does len(job.result()) return, and how is the second PUB's data accessed?

A. 1; all PUBs merge into result[0]
B. 3; via result[1].data
C. 3; via result.pubs[2]
D. 2; the identical PUBs are deduplicated

Q62. After a hardware run, a researcher must report consumed QPU time for a grant. Which call gives it?

A. job.status().qpu_time
B. job.result().metadata["wall_clock"]
C. len(job.result()) * shots
D. job.usage() (with job.metrics() for detailed timestamps)

Q63. Counts for a 2-qubit circuit are {'00': 400, '01': 100, '10': 100, '11': 400} over 1000 shots. What is the manual estimate of ⟨ZZ⟩?

A. 0.8
B. 0.0
C. 0.6 — even-parity strings count +1, odd-parity strings count −1
D. -0.6

Q64. An ideal simulator gives a GHZ circuit only '000' and '111', but the hardware histogram also shows small bars at '001', '010', '110', etc. What is the best explanation?

A. Gate errors and readout errors on the device populate outcomes that are impossible ideally
B. The hardware uses big-endian ordering, so the extra strings are relabeled ideal outcomes
C. measure_all() measured the ancilla qubits too
D. The transpiler added SWAPs, which change the sampled distribution

Section 8 — Operate with OpenQASM (Q65–Q68)

Q65. What does qiskit.qasm3.dumps(qc) output for a Bell circuit built as QuantumCircuit(2, 2) with h(0), cx(0, 1), and measure([0, 1], [0, 1])?

OPENQASM 2.0;
include "qelib1.inc";
qreg q[2];
creg c[2];
h q[0];
cx q[0],q[1];
measure q -> c;

OPENQASM 3.0;
include "stdgates.inc";
bit[2] c;
qubit[2] q;
h q[0];
cx q[0], q[1];
c[0] = measure q[0];
c[1] = measure q[1];

OPENQASM 3.0;
qubit q[2];
bit c[2];
H q[0];
CX q[0], q[1];
measure q -> c;

OPENQASM 3.0;
include "stdgates.inc";
qreg q[2];
creg c[2];
h q[0];
cx q[0], q[1];
c = measure q;

Q66. This OpenQASM 2 program is loaded with qiskit.qasm2.loads and run on an ideal simulator with many shots:

OPENQASM 2.0;
include "qelib1.inc";
qreg q[2];
creg c[2];
x q[0];
h q[1];
cx q[1],q[0];
measure q -> c;

Which distribution results?

A. {'11': ~50%, '00': ~50%}
B. {'01': 100%}
C. {'01': ~50%, '10': ~50%}
D. {'11': 100%}

Q67. Which capability exists in OpenQASM 3 but NOT in OpenQASM 2?

A. The include statement
B. Two-qubit gates such as cx
C. Classical registers
D. Typed classical data, input parameters, and classical control flow (e.g., if/while blocks)

Q68. A collaborator emails the file teleport.qasm containing an OpenQASM 3 program. Which snippet turns it into a QuantumCircuit?

A. from qiskit import qasm3; qc = qasm3.load("teleport.qasm")
B. qc = qasm3.loads("teleport.qasm")
C. qc = QuantumCircuit.from_qasm_file_v3("teleport.qasm")
D. qc = qasm3.dump("teleport.qasm")

End of Paper 10. Check your answers against paper-10-FULL-answers.md. Target: 47+ to pass; 58+ means you are exam-ready with margin.