Section 5-6: Use the sampler/estimator primitive

TASK 5.1/6.1: Set sampler/estimator primitive options¶

Which snippet correctly transpiles a parameterized circuit for a chosen backend and produces an ISA circuit before using Estimator V2?

a.

from qiskit.transpiler import generate_preset_pass_manager
pm = generate_preset_pass_manager(optimization_level=1, backend=backend)
isa_circ = pm.run(circ)

b.

isa_circ = circ  # QPUs accept any gates; transpilation is optional

c.

from qiskit import transpile
isa_circ = transpile(circ)  # omit backend

d.

pm = generate_preset_pass_manager(backend=None)
isa_circ = pm.run(circ.decompose())

You need to configure the Sampler to use 4096 shots by default for all runs in a session. Which method should you use?

a. sampler.options.default_shots = 4096
b. sampler.set_shots(4096)
c. sampler.options.shots.default = 4096
d. sampler.run(..., shots=4096)

Which call correctly submits work to Estimator V2 using the Primitive Unified Bloc (PUB) tuple?

a.

job = estimator.run([(isa_circ, isa_obs, param_values)])

b.

job = estimator.run([(isa_obs, isa_circ, param_values)])

c.

job = estimator.run([(isa_circ, param_values)])

d.

job = estimator.run((isa_circ, isa_obs, param_values))

For Sampler V2, which preparation is correct before transpilation and submission?

a.

circ.measure_all()
pm = generate_preset_pass_manager(optimization_level=1, backend=backend)
isa_circ = pm.run(circ)
job = sampler.run([(isa_circ, param_values)])

b.

pm = generate_preset_pass_manager(optimization_level=3, backend=backend)
isa_circ = pm.run(circ)  # no measurements needed
job = sampler.run([(isa_circ,)])

c.

job = sampler.run([(circ,)])

d.

isa_circ = circ.remove_final_measurements(inplace=True)
job = sampler.run([(isa_circ,)])

Which initialization correctly selects the execution mode consistent with the examples?

a.

from qiskit_ibm_runtime import EstimatorV2 as Estimator
estimator = Estimator(mode=backend)

b.

from qiskit_ibm_runtime import EstimatorV2 as Estimator
estimator = Estimator(mode="session")  # string literal

c.

from qiskit_ibm_runtime import EstimatorV2 as Estimator
estimator = Estimator()  # mode is mandatory

d.

from qiskit_ibm_runtime import EstimatorV2 as Estimator
estimator = Estimator(mode="batch").run(backend)

How can you request a backend that supports fractional gates per the guide?

a.

service = QiskitRuntimeService()
backend = QiskitRuntimeService(use_fractional_gates=True)

b.

service = QiskitRuntimeService()
backend = service.get_backend("fractional-gates")

c.

service = QiskitRuntimeService()
backend = service.least_busy(fractional=True)

d.

service = QiskitRuntimeService()
backend = service.least_busy(use_fractional_gates=True)

Which code path best reflects a minimal, correct optimization/transpilation workflow before running primitives?

a. Create circuit → generate_preset_pass_manager(optimization_level=1, backend) → pm.run(circuit) → align observable with apply_layout → Estimator.run([...])
b. Create circuit → call Estimator.run(circuit) and let the service infer gates automatically
c. Create circuit → decompose to basis gates locally without a backend → Estimator.run([...])
d. Create circuit → add barriers to prevent changes → Estimator.run([...])

Which code correctly enables dynamical decoupling (DD) in Sampler V2 and selects the XpXm sequence?

a.

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

b.

sampler.options.resilience.zne_mitigation = True
sampler.options.resilience.zne.extrapolator = "exponential"

c.

sampler.options.twirling.enable_gates = True
sampler.options.twirling.sequence_type = "XpXm"

d.

sampler.set_options(dynamical_decoupling=True, sequence_type="XpXm")

You want to randomize two‑qubit gate errors via Pauli twirling when running the Sampler. Which method most directly enables this according to the twirling options API?

a. sampler.options.twirling = {"circuit": {"enable": True}}
b. sampler.options.twirling.enable = True
c. sampler.options.transpilation.pauli_twirling = True
d. sampler.enable_pauli_twirling()

When is enabling dynamical decoupling most likely to help for Sampler runs on hardware?

a. Only when running on a simulator with noise disabled
b. When all qubits are busy almost all the time (densely packed schedules)
c. When circuits contain idle gaps on some qubits where no operations occur
d. Only when measuring expectation values with Estimator

Which error‑related options are supported directly by Sampler V2?

a. Pauli twirling (suppression) via sampler.options.twirling.*
b. TREX measurement mitigation via sampler.options.resilience.measure_mitigation = True
c. Zero‑noise extrapolation via sampler.options.resilience.zne_mitigation = True
d. Probabilistic error cancellation via sampler.options.resilience.pec_mitigation = True

Which snippet correctly configures Pauli twirling in Sampler V2 with 32 randomizations and 100 shots per randomization?

a.

sampler.options.twirling.enable_gates = True
sampler.options.twirling.num_randomizations = 32
sampler.options.twirling.shots_per_randomization = 100

b.

sampler.options.twirling.enable = True
sampler.options.twirling.count = 32
sampler.options.twirling.shots = 100

c.

sampler.options.resilience.twirling = True
sampler.options.resilience.num_randomizations = 32
sampler.options.resilience.shots_per_randomization = 100

d.

sampler.enable_twirling(32, 100)

How do you set a repetition delay of 0.5 ms between shots for Sampler V2?

a. sampler.options.execution.rep_delay = 0.5
b. sampler.options.environment.rep_delay = 0.5
c. sampler.options.execution.rep_delay = 0.0005
d. sampler.set_options(rep_delay_ms=0.5)

When calling SamplerV2.run, what is the correct data type for the first positional argument?

a. A single QuantumCircuit instance
b. A list of ISA circuits accepted by the runtime ([isa_circuit, ...])
c. A Distribution object
d. A dictionary mapping bitstrings to probabilities

Which statement about dynamical decoupling is TRUE?

a. DD is a measurement‑error mitigation method that post‑processes bitstrings
b. Each inserted DD pulse sequence ideally implements an identity operation while suppressing coherent errors on idling qubits
c. DD is guaranteed to improve results in all cases, even with dense schedules
d. DD can only be used with Estimator, not with Sampler

In EstimatorV2, what does options.default_precision control and what is its default value?

a. It sets the target standard error for expectation values (used when shots aren’t given); default is 0.015625 (1/√4096).
b. It sets the transpiler optimization level; default is 1.
c. It fixes the number of shots for each circuit configuration; default is 4096.
d. It controls backend run priority; default is “normal”.

Regarding options.default_shots in EstimatorV2, which statement is correct?

a. If set, it overrides default_precision, and when twirling is enabled it is split across randomizations.
b. It is ignored whenever twirling is enabled.
c. It only applies to simulators and is ignored on hardware.
d. It sets the maximum number of shots per job but never overrides precision.

Which mapping of resilience_level to behavior is correct for EstimatorV2?

a. 0: No mitigation; 1: Readout mitigation + measurement twirling; 2: Adds bias‑reducing estimator mitigation (medium cost).
b. 0: Readout mitigation only; 1: Full error correction; 2: No mitigation.
c. 0: Measurement twirling; 1: Probabilistic error cancellation; 2: Zero‑noise extrapolation only.
d. 0: No mitigation; 1: Full QEC; 2: Hardware calibration reset only.

For TwirlingOptions.strategy, what best describes the default "active-accum" behavior?

a. In each twirled layer, twirl the union of instruction qubits encountered up to that layer.
b. Twirl only the instruction qubits of the current layer, ignoring earlier ones.
c. Twirl all qubits in the circuit at every twirled layer.
d. Twirl only the first two qubits of the circuit to minimize overhead.

What is the default of TwirlingOptions.enable_measure and where does it apply?

a. True for Estimator, False for Sampler; enables twirling on measurement instructions not inside conditionals.
b. True for both Estimator and Sampler; always twirl all measurements.
c. False for both primitives; measurement twirling must be enabled via resilience_level only.
d. True only on simulators; False on hardware backends.

When options.resilience.zne.amplifier='pea' is selected, which effect is correct?

a. The runtime always uses twirling and performs layer noise learning before executing amplified circuits.
b. ZNE is disabled because PEA conflicts with twirling.
c. Only single‑qubit gates are folded; two‑qubit gates are untouched.
d. The extrapolator is forced to 'fallback'.

What are the documented defaults for options.resilience.zne.noise_factors?

a. (1, 1.5, 2) for PEA and (1, 3, 5) otherwise.
b. (1, 2, 4) for PEA and (1, 3, 9) otherwise.
c. Always (1, 3, 5) regardless of amplifier.
d. Determined solely by default_precision.

When ZNE options are enabled in EstimatorV2, which additional data fields are returned per PUB result?

a. evs_extrapolated/stds_extrapolated and evs_noise_factors/stds_noise_factors/ensemble_stds_noise_factors.
b. Only calibration_matrix with no standard deviations.
c. zne_trace strings and fit_r2 only.
d. No additional data; ZNE affects only evs/stds.

Which snippet correctly runs SamplerV2 on two circuits and obtains quasi‑probability results?

a.

from qiskit_ibm_runtime import SamplerV2
sampler = SamplerV2(mode=backend)
job = sampler.run([circ1_isa, circ2_isa])
result = job.result()
dists = result[0].data, result[1].data

b.

from qiskit_ibm_runtime import SamplerV2
sampler = SamplerV2(mode=backend)
job = sampler.run(circ1_isa, circ2_isa)
dists = job.result().distributions

c.

from qiskit_ibm_runtime import SamplerV2
sampler = SamplerV2(mode=backend)
result = sampler.run([circ1_isa, circ2_isa], runs=2048)
dists = result.data

d.

from qiskit_ibm_runtime import SamplerV2
sampler = SamplerV2(mode=backend)
job = sampler.run([circ1, circ2])  # QuantumCircuit objects
dists = job.result()

What is options.seed_estimator used for in EstimatorV2?

a. To control sampling randomness (e.g., shot sampling and randomizations) via a fixed seed.
b. To seed the transpiler’s layout selection.
c. To fix the hardware qubit mapping across sessions.
d. To seed the optimizer used in VQE.

TASK 5.2/6.2: Understand the theoretical background behind the sampler/estimator primitive¶

Which snippet best demonstrates multiple PUBs in one call to Sampler V2?

a.

pubs = [(qc1, [theta1], 2000), (qc2, [theta2], 4000)]
job = sampler.run(pubs)
res = job.result()

b.

pubs = [(qc1, obs1, [theta1]), (qc2, obs2, [theta2])]
job = sampler.run(pubs)

c.

pubs = [([qc1, qc2], {'shots': [2000, 4000]})]
job = sampler.run(pubs)

d.

pubs = {qc1: 2000, qc2: 4000}
job = sampler.run(pubs)

Which of the following best describes the output of the Sampler primitive?

a. A histogram of expectation values for given observables
b. A quasi-probability distribution over bitstrings measured from the circuit
c. A sequence of transpiled circuits optimized for the backend
d. A set of error-mitigated observables in operator form

You need to obtain shot-by-shot samples from a circuit while preserving the measurement order for dynamic-circuit compatibility. Which method should you use?

a. Use EstimatorV2.run([qc]) to return expectation values per shot.
b. Use SamplerV1.run([qc]) to return a quasi-probability distribution.
c. Use SamplerV2.run([qc]) to return samples of classical outcomes, preserving shot order.
d. Use QuantumCircuit.sample_counts(qc) to return per-shot bit arrays.

You want to submit several circuits, each with its own parameter values and (optionally) shots, in a single call. Which interface best matches the Sampler V2 design?

a. Provide a list of PUBs, where each PUB is (circuit, <optional> parameter_values, <optional> shots>).
b. Provide a list of (observable, circuit) pairs.
c. Provide a dictionary mapping circuits to quasi-probabilities.
d. Provide a single circuit with a batch size argument batch=True.

In Sampler V2, results are organized by classical register names from the circuit. Which description best matches this behavior?

a. Samples are returned as raw bytes, with no register structure available.
b. Samples are grouped per classical register, aiding compatibility with dynamic circuits.
c. Samples are flattened into integers and sorted by frequency.
d. Samples are returned only as aggregate counts per register.

In the context of the Estimator primitive, what is the main theoretical effect of Pauli twirling on gate errors?

a. It only applies to single-qubit gates and leaves two-qubit noise unchanged.
b. It eliminates measurement (readout) errors by repeating measurements with majority voting.
c. It exactly cancels hardware noise by inverting it gate-by-gate.
d. It transforms arbitrary noise into a Pauli channel so that coherent errors accumulate linearly rather than quadratically.

You estimate expectation values of Pauli observables and see bias dominated by readout noise. Which technique directly targets measurement errors for Estimator?

a. Pauli twirling (gate twirling)
b. Twirled Readout Error eXtinction (TREX)
c. Dynamical decoupling (DD)
d. Zero-noise extrapolation (ZNE)

Zero-noise extrapolation (ZNE), as used with the Estimator, is best summarized by which two-stage process?

a. Learn a quasi-probability model and sample from it to reproduce the ideal circuit exactly.
b. Amplify noise (e.g., by digital gate folding) and then extrapolate expectation values to the zero-noise limit.
c. Insert idle-pulse sequences to cancel coherent errors during “gaps” in the schedule.
d. Calibrate a confusion matrix and invert it to de-bias measurement outcomes.

In digital gate folding for ZNE, replacing a unitary $U$ by $UU^{\dagger}U$ corresponds to which noise amplification factor?

a. 3
b. 2
c. 1
d. 0

Probabilistic Error Amplification (PEA) provides a more accurate noise amplification than simple folding. Which statement captures its core idea?

a. It learns a twirled noise model for each entangling layer and then injects single-qubit noise proportionally during amplification.
b. It only repeats two-qubit gates and their inverses to scale noise without any learning.
c. It yields an exactly unbiased estimator of the expectation value without overhead.
d. It does not require ZNE to be enabled because it is a suppression (not mitigation) method.

You need an unbiased estimator of ⟨O⟩ but can tolerate the highest shot overhead. Which mitigation method matches this requirement?

a. ZNE with linear extrapolation
b. PEC (probabilistic error cancellation)
c. TREX with many randomizations
d. Gate twirling only

In Pauli gate twirling as implemented for Estimator runs, how are randomized circuit instances and shots typically managed?

a. They change the backend’s native basis gates to Pauli-only operations.
b. Randomizations only affect calibration circuits and never the main circuit instances.
c. The parameters set the ZNE noise factors and the extrapolator form.
d. The Estimator samples multiple randomized instances (controlled by num_randomizations) and takes shots_per_randomization shots from each.

For a Hermitian observable and real-valued expectation ⟨O⟩, what is the expected data type of the Estimator’s returned value (ignoring confidence intervals and metadata)?

a. A dictionary mapping bitstrings to counts
b. A complex number with generally nonzero imaginary part
c. A real scalar (float) expectation value
d. A list of complex amplitudes (statevector)

Conceptually, how do error suppression and error mitigation differ for Estimator‑based workflows?

a. Suppression modifies the implemented circuit/pulse schedule to reduce noise during execution (e.g., DD, gate twirling), whereas mitigation post‑processes or re‑processes experimental data to adjust expectation values (e.g., TREX, ZNE, PEC).
b. Both terms mean the same thing and are interchangeable in practice.
c. Mitigation changes gate calibrations in hardware; suppression extrapolates to the zero‑noise limit.
d. Suppression is only about measurement, while mitigation is only about two‑qubit gates.

Which Estimator option enables measurement error mitigation via TREX according to the documented resilience settings?

a. estimator.options.twirling.enable_gates = True
b. estimator.options.resilience.measure_mitigation = True
c. estimator.options.dynamical_decoupling.enable = True
d. estimator.options.resilience.zne_mitigation = True

You want ZNE with specific amplification factors and an exponential extrapolator. Which option pair matches the documented keys?

a. estimator.options.zne.noise_factors, estimator.options.zne.extrapolator
b. estimator.options.resilience.zne.noise_factors, estimator.options.resilience.zne.extrapolator
c. estimator.options.zne.factors, estimator.options.zne.method='exponential'
d. estimator.options.resilience.zne.factors, estimator.options.resilience.zne.fit='exp'

TASK 5.1/6.1: Set sampler/estimator primitive options¶

What are fractional gates¶

When to use¶

When not to use (and why)¶

Dynamic Decoupling¶

Pauli twirling¶

Coherent vs. Incoherent errors¶

TASK 5.2/6.2: Understand the theoretical background behind the sampler/estimator primitive¶