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# Primitives (qiskit.primitives)¶

## Overview of Estimator¶

Estimator class estimates expectation values of quantum circuits and observables.

An estimator is initialized with an empty parameter set. The estimator is used to create a JobV1, via the qiskit.primitives.Estimator.run() method. This method is called with the following parameters

• quantum circuits ($$\psi_i(\theta)$$): list of (parameterized) quantum circuits (a list of QuantumCircuit objects).

• observables ($$H_j$$): a list of SparsePauliOp objects.

• parameter values ($$\theta_k$$): list of sets of values to be bound to the parameters of the quantum circuits (list of list of float).

The method returns a JobV1 object, calling qiskit.providers.JobV1.result() yields the a list of expectation values plus optional metadata like confidence intervals for the estimation.

$\langle\psi_i(\theta_k)|H_j|\psi_i(\theta_k)\rangle$

Here is an example of how the estimator is used.

from qiskit.primitives import Estimator
from qiskit.circuit.library import RealAmplitudes
from qiskit.quantum_info import SparsePauliOp

psi1 = RealAmplitudes(num_qubits=2, reps=2)
psi2 = RealAmplitudes(num_qubits=2, reps=3)

H1 = SparsePauliOp.from_list([("II", 1), ("IZ", 2), ("XI", 3)])
H2 = SparsePauliOp.from_list([("IZ", 1)])
H3 = SparsePauliOp.from_list([("ZI", 1), ("ZZ", 1)])

theta1 = [0, 1, 1, 2, 3, 5]
theta2 = [0, 1, 1, 2, 3, 5, 8, 13]
theta3 = [1, 2, 3, 4, 5, 6]

estimator = Estimator()

# calculate [ <psi1(theta1)|H1|psi1(theta1)> ]
job = estimator.run([psi1], [H1], [theta1])
job_result = job.result() # It will block until the job finishes.
print(f"The primitive-job finished with result {job_result}"))

# calculate [ <psi1(theta1)|H1|psi1(theta1)>,
#             <psi2(theta2)|H2|psi2(theta2)>,
#             <psi1(theta3)|H3|psi1(theta3)> ]
job2 = estimator.run([psi1, psi2, psi1], [H1, H2, H3], [theta1, theta2, theta3])
job_result = job2.result()
print(f"The primitive-job finished with result {job_result}")


## Overview of Sampler¶

Sampler class calculates probabilities or quasi-probabilities of bitstrings from quantum circuits.

A sampler is initialized with an empty parameter set. The sampler is used to create a JobV1, via the qiskit.primitives.Sampler.run() method. This method is called with the following parameters

• quantum circuits ($$\psi_i(\theta)$$): list of (parameterized) quantum circuits. (a list of QuantumCircuit objects)

• parameter values ($$\theta_k$$): list of sets of parameter values to be bound to the parameters of the quantum circuits. (list of list of float)

The method returns a JobV1 object, calling qiskit.providers.JobV1.result() yields a SamplerResult object, which contains probabilities or quasi-probabilities of bitstrings, plus optional metadata like error bars in the samples.

Here is an example of how sampler is used.

from qiskit.primitives import Sampler
from qiskit import QuantumCircuit
from qiskit.circuit.library import RealAmplitudes

# a Bell circuit
bell = QuantumCircuit(2)
bell.h(0)
bell.cx(0, 1)
bell.measure_all()

# two parameterized circuits
pqc = RealAmplitudes(num_qubits=2, reps=2)
pqc.measure_all()
pqc2 = RealAmplitudes(num_qubits=2, reps=3)
pqc2.measure_all()

theta1 = [0, 1, 1, 2, 3, 5]
theta2 = [0, 1, 2, 3, 4, 5, 6, 7]

# initialization of the sampler
sampler = Sampler()

# Sampler runs a job on the Bell circuit
job = sampler.run(circuits=[bell], parameter_values=[[]], parameters=[[]])
job_result = job.result()
print([q.binary_probabilities() for q in job_result.quasi_dists])

# Sampler runs a job on the parameterized circuits
job2 = sampler.run(
circuits=[pqc, pqc2],
parameter_values=[theta1, theta2],
parameters=[pqc.parameters, pqc2.parameters])
job_result = job2.result()
print([q.binary_probabilities() for q in job_result.quasi_dists])


## Estimator¶

 BaseEstimator([circuits, observables, ...]) Estimator base class. Estimator([circuits, observables, ...]) Reference implementation of BaseEstimator. BackendEstimator(backend[, options, ...]) Evaluates expectation value using Pauli rotation gates.

## Sampler¶

 BaseSampler([circuits, parameters, options]) Sampler base class Sampler([circuits, parameters, options]) Sampler class. BackendSampler(backend[, options, ...]) A BaseSampler implementation that provides an interface for leveraging the sampler interface from any backend.

## Results¶

 EstimatorResult(values, metadata) Result of Estimator. SamplerResult(quasi_dists, metadata) Result of Sampler.