Qiskit/qiskit_humaneval_hard huggingface dataset:
Return the list of names of all the fake providers of type FakeBackendV2 which contains ecr gates in its available operations.
You must implement this using a function named `fake_providers_v2_with_ecr` with no arguments.

Solution:
import importlib
import inspect
from qiskit_ibm_runtime.fake_provider import fake_backend

def fake_providers_v2_with_ecr():
    fake_provider_module = importlib.import_module("qiskit_ibm_runtime.fake_provider")
    fake_providers = {}
    for name, obj in inspect.getmembers(fake_provider_module):
        if inspect.isclass(obj) and issubclass(obj, fake_backend.FakeBackendV2):
            fake_providers[name] = obj
    fake_providers_ecr = []
    for name, provider in fake_providers.items():
        backend = provider()
        if "ecr" in backend.operation_names:
            fake_providers_ecr.append(name)
    return fake_providers_ecr


Test:
import importlib
import inspect
from qiskit_ibm_runtime.fake_provider import fake_backend
def check(candidate):
    providers_can = candidate()
    providers_exp = [
        "FakeCusco",
        "FakeKawasaki",
        "FakeKyiv",
        "FakeKyoto",
        "FakeOsaka",
        "FakePeekskill",
        "FakeQuebec",
        "FakeSherbrooke",
        "FakeBrisbane",
        "FakeCairoV2",
    ]
    for providers in providers_can:
        assert providers in providers_exp
    for providers in providers_exp:
        assert providers in providers_can

check(fake_providers_v2_with_ecr)
Transpile the 4-qubit QFT circuit using preset passmanager with optimization level 3 and seed transpiler = 1234 in FakeOsaka, FakeSherbrooke and FakeBrisbane. Compute the cost of the instructions by penalizing the two qubit gate with a cost of 5, rz gates with a cost 1 and other gates with a cost 2 and return the value of the highest cost among these backends.
You must implement this using a function named `backend_with_lowest_complexity` with no arguments.

Solution:
from qiskit_ibm_runtime.fake_provider import FakeOsaka, FakeSherbrooke, FakeBrisbane
from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager
from qiskit.circuit.library import QFT

def backend_with_lowest_complexity():
    qc = QFT(4)
    backends = [FakeOsaka(), FakeSherbrooke(), FakeBrisbane()]
    complexity_dict = {}
    for backend in backends:
        pm = generate_preset_pass_manager(
            optimization_level=3, seed_transpiler=1234, backend=backend
        )
        data = pm.run(qc).data
        complexity = 0
        for instruc in data:
            if instruc.operation.num_qubits == 2:
                complexity += 5
            elif instruc.operation.name == "rz":
                complexity += 1
            else:
                complexity += 2
        complexity_dict[backend.name] = complexity
    return complexity_dict[max(complexity_dict, key=complexity_dict.get)]


Test:
from qiskit_ibm_runtime.fake_provider import FakeOsaka, FakeSherbrooke, FakeBrisbane
from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager
from qiskit.circuit.library import QFT
def check(candidate):
    complexity_can = candidate()
    complexity_exp = 194
    assert complexity_can == complexity_exp

check(backend_with_lowest_complexity)
Initialize a CNOTDihedral element from a QuantumCircuit consist of 2-qubits with cx gate on qubit 0 and 1 and t gate on qubit 0 and return.
You must implement this using a function named `initialize_cnot_dihedral` with no arguments.

Solution:
from qiskit import QuantumCircuit
from qiskit.quantum_info import CNOTDihedral

def initialize_cnot_dihedral():
    circ = QuantumCircuit(2)
    # Apply gates
    circ.cx(0, 1)
    circ.t(0)
    elem = CNOTDihedral(circ)

    return elem


Test:
from qiskit import QuantumCircuit
from qiskit.quantum_info import CNOTDihedral
def check(candidate):
    result = candidate()
    assert isinstance(result, CNOTDihedral), f'Expected result to be CNOTDihedral, but got {type(result)}'
    assert result.linear.tolist() == [[1, 0], [1, 1]]
    assert str(result.poly) == "0 + x_0"
    assert result.shift.tolist() == [0, 0]

check(initialize_cnot_dihedral)
Create two Quantum Circuits of 2 qubits. First quantum circuit should have a cx gate on qubits 0 and 1 and a T gate on qubit 0. The second one is the same but with an additional X gate on qubit 1. Convert the two quantum circuits into CNOTDihedral elements and return the composed circuit.
You must implement this using a function named `compose_cnot_dihedral` with no arguments.

Solution:
from qiskit import QuantumCircuit
from qiskit.quantum_info import CNOTDihedral

def compose_cnot_dihedral():
    circ1 = QuantumCircuit(2)
    # Apply gates
    circ1.cx(0, 1)
    circ1.t(0)
    elem1 = CNOTDihedral(circ1)
    circ2 = circ1.copy()
    circ2.x(1)
    elem2 = CNOTDihedral(circ2)
    composed_elem = elem1.compose(elem2)
    return composed_elem


Test:
from qiskit import QuantumCircuit
from qiskit.quantum_info import CNOTDihedral
def check(candidate):
    result = candidate()
    assert isinstance(result, CNOTDihedral), f'Expected result to be CNOTDihedral, but got {type(result)}'
    assert result.linear.tolist() == [[1, 0], [0, 1]]
    assert str(result.poly) == "0 + 2*x_0"
    assert list(result.shift) == [0, 1]

check(compose_cnot_dihedral)
Create two ScalarOp objects with dimension 2 and coefficient 2, compose them together, and return the resulting ScalarOp.
You must implement this using a function named `compose_scalar_ops` with no arguments.

Solution:
from qiskit.quantum_info import ScalarOp

def compose_scalar_ops():
    op1 = ScalarOp(2, 2)
    op2 = ScalarOp(2, 2)
    composed_op = op1.compose(op2)
    return composed_op


Test:
from qiskit.quantum_info import ScalarOp
def check(candidate):
    result = candidate()
    assert isinstance(result, ScalarOp), f'Expected result to be ScalarOp, but got {type(result)}'
    assert result.coeff == 4
    assert result.input_dims() == (2,)

check(compose_scalar_ops)
Initialize Choi matrices for the given data1 and data2 as inputs. Compute data1 adjoint, and then return the data1 Choi matrix, its adjoint and the composed choi matrices in order.
You must implement this using a function named `initialize_adjoint_and_compose` with the following arguments: data1, data2.

Solution:
from qiskit.quantum_info import Choi
import numpy as np

def initialize_adjoint_and_compose(data1, data2):
    choi1 = Choi(data1)
    choi2 = Choi(data2)
    adjoint_choi1 = choi1.adjoint()
    composed_choi = choi1.compose(choi2)
    return choi1, adjoint_choi1, composed_choi


Test:
from qiskit.quantum_info import Choi
import numpy as np
def check(candidate):
    data = np.eye(4)
    choi, adjoint_choi, composed_choi = candidate(data, data)
    assert isinstance(choi, Choi), f'Expected choi to be Choi, but got {type(choi)}'
    assert choi.dim == (2, 2), f'Expected dimensions to be (2, 2), but got {choi.dim}'
    assert isinstance(adjoint_choi, Choi), f'Expected adjoint_choi to be Choi, but got {type(adjoint_choi)}'
    assert isinstance(composed_choi, Choi), f'Expected composed_choi to be Choi, but got {type(composed_choi)}'
    expected_adjoint_data = data.conj().T
    assert np.allclose(adjoint_choi.data, expected_adjoint_data), f'Expected adjoint data to be {expected_adjoint_data}, but got {adjoint_choi.data}'
check(initialize_adjoint_and_compose)
Create a parameterized quantum circuit using minimum resources whose statevector output cover the equatorial plane of the surface of the bloch sphere.
You must implement this using a function named `circuit` with no arguments.

Solution:
from qiskit.circuit import QuantumCircuit, Parameter

def circuit():
    qc = QuantumCircuit(1)
    qc.h(0)
    theta = Parameter('th')
    qc.rz(theta,0)
    return qc
    

Test:
from qiskit.circuit import QuantumCircuit, Parameter
def check(candidate):
    import numpy as np
    from qiskit.quantum_info import Statevector
    def statevector_to_bloch_angles(state_vector):
        alpha = state_vector[0]
        beta = state_vector[1]
        norm = np.sqrt(np.abs(alpha)**2 + np.abs(beta)**2)
        alpha = alpha / norm
        beta = beta / norm
        theta = 2 * np.arccos(np.abs(alpha))
        phi = np.angle(beta) - np.angle(alpha)
        phi = (phi + 2 * np.pi) % (2 * np.pi)
        return theta, phi
    error = 0.000001
    for i in range(1000):
        qc = candidate()
        num_params = qc.num_parameters
        qc.assign_parameters(np.random.randn(num_params), inplace=True)
        sv = Statevector(qc)
        theta, phi = statevector_to_bloch_angles(sv)
        assert np.pi/2 - error <= theta <= np.pi/2 + error
    
check(circuit)
Given a clifford circuit return a list of n random clifford circuits which are equivalent to the given circuit up to a relative and absolute tolerance of 0.4.
You must implement this using a function named `equivalent_clifford_circuit` with the following arguments: circuit, n.

Solution:
from qiskit import QuantumCircuit
from qiskit.quantum_info import random_clifford, Operator

def equivalent_clifford_circuit(circuit, n):
    op_or = Operator(circuit)
    num_qubits = circuit.num_qubits
    qc_list = []
    counter = 0
    while counter< n:
        qc = random_clifford(num_qubits).to_circuit()
        op_qc = Operator(qc)
        if op_qc.equiv(op_or, rtol = 0.4, atol = 0.4) == True:
            counter += 1
            qc_list.append(qc)
    return qc_list


Test:
from qiskit import QuantumCircuit
from qiskit.quantum_info import random_clifford, Operator
def check(candidate):
    from qiskit.quantum_info import Clifford
    qc_comp = random_clifford(5).to_circuit()
    op_comp = Operator(qc_comp)
    can_circ_list = candidate(qc_comp, 10)
    for item in can_circ_list:
        assert Operator(item).equiv(op_comp, rtol = 0.4, atol = 0.4)
        try:
            Clifford(item)
        except Exception as err:
            raise AssertionError("The circuit is not a Clifford circuit.") from err

check(equivalent_clifford_circuit)
Return an ansatz to create a quantum dataset of pure states distributed equally across the bloch sphere. Use minimum number of gates in the ansatz.
You must implement this using a function named `circuit` with no arguments.

Solution:
from qiskit.circuit import QuantumCircuit, Parameter

def circuit():
    qc = QuantumCircuit(1)
    p1 = Parameter("p1")
    p2 = Parameter("p2")
    qc.rx(p1,0)
    qc.ry(p2,0)
    return qc


Test:
from qiskit.circuit import QuantumCircuit, Parameter
def check(candidate):
    assert candidate().num_parameters >= 2 , "The circuit doesn't cover the bloch sphere."
    assert candidate().num_parameters <= 5 , "The circuit is too long"

check(circuit)
Create a quantum circuit using LieTrotter for a list of Pauli strings and times. Each Pauli string is associated with a corresponding time in the 'times' list. The function should return the resulting QuantumCircuit.
You must implement this using a function named `create_product_formula_circuit` with the following arguments: pauli_strings, times, order, reps.

Solution:
from qiskit.quantum_info import Operator
from qiskit.circuit.library import PauliEvolutionGate
from qiskit.synthesis import LieTrotter
from qiskit import QuantumCircuit
from qiskit.quantum_info import Pauli, SparsePauliOp

def create_product_formula_circuit(pauli_strings, times, order, reps):
    qc = QuantumCircuit(len(pauli_strings[0]))
    synthesizer = LieTrotter(reps=reps)
    for pauli_string, time in zip(pauli_strings, times):
        pauli = Pauli(pauli_string)
        hamiltonian = SparsePauliOp(pauli)
        evolution_gate = PauliEvolutionGate(hamiltonian, time)
        synthesized_circuit = synthesizer.synthesize(evolution_gate)
        qc.append(synthesized_circuit.to_gate(), range(len(pauli_string)))
    return qc


Test:
from qiskit.quantum_info import Operator
from qiskit.circuit.library import PauliEvolutionGate
from qiskit.synthesis import LieTrotter
from qiskit import QuantumCircuit
from qiskit.quantum_info import Pauli, SparsePauliOp
def check(candidate):
    pauli_strings = ["X", "Y", "Z"]
    times = [1.0, 2.0, 3.0]
    order = 2
    reps = 1

    def create_solution_circuit(pauli_strings, times, order, reps):
        qc = QuantumCircuit(len(pauli_strings[0]))
        synthesizer = LieTrotter(reps=reps)
        for pauli_string, time in zip(pauli_strings, times):
            pauli = Pauli(pauli_string)
            hamiltonian = SparsePauliOp(pauli)
            evolution_gate = PauliEvolutionGate(hamiltonian, time)
            synthesized_circuit = synthesizer.synthesize(evolution_gate)
            qc.append(synthesized_circuit.to_gate(), range(len(pauli_string)))
        return qc

    solution_circuit = create_solution_circuit(pauli_strings, times, order, reps)
    candidate_circuit = candidate(pauli_strings, times, order, reps)

    assert Operator(solution_circuit) == Operator(candidate_circuit), "The candidate circuit does not match the expected solution."
    assert isinstance(candidate_circuit, QuantumCircuit), "The returned object is not a QuantumCircuit."

check(create_product_formula_circuit)
Remove barriers from the given quantum circuit and calculate the depth before and after removal.
Return a PropertySet with 'depth_before', 'depth_after', and 'width' properties.
The function should only remove barriers and not perform any other optimizations.
You must implement this using a function named `calculate_depth_after_barrier_removal` with the following arguments: qc.

Solution:
from qiskit import QuantumCircuit
from qiskit.transpiler import PassManager, PropertySet
from qiskit.transpiler.passes import RemoveBarriers

def calculate_depth_after_barrier_removal(qc):
    property_set = PropertySet()
    property_set["depth_before"] = qc.depth()
    property_set["width"] = qc.width()
    
    pass_manager = PassManager(RemoveBarriers())
    optimized_qc = pass_manager.run(qc)
    
    property_set['depth_after'] = optimized_qc.depth()
    
    return property_set


Test:
from qiskit import QuantumCircuit
from qiskit.transpiler import PassManager, PropertySet
from qiskit.transpiler.passes import RemoveBarriers
def check(candidate):
    qc = QuantumCircuit(3)
    qc.h(0)
    qc.barrier()
    qc.cx(0, 1)
    qc.barrier()
    qc.cx(1, 2)
    qc.measure_all()
    
    property_set = candidate(qc)
    
    assert property_set["depth_before"] == qc.depth(), "'depth_before' should match the original circuit depth"
    assert property_set["width"] == qc.width(), "'width' should match the circuit width"
    optimized_qc = PassManager(RemoveBarriers()).run(qc)
    assert property_set["depth_after"] == optimized_qc.depth(), "'depth_after' should match the depth of a barrier-free circuit"

check(calculate_depth_after_barrier_removal)
Create a CouplingMap with a specific coupling list, then modify it by adding an edge and a physical qubit.
The initial coupling list is [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5]].
Add an edge (5, 6), and add a physical qubit "7".
You must implement this using a function named `create_and_modify_coupling_map` with no arguments.

Solution:
from qiskit.transpiler import CouplingMap

def create_and_modify_coupling_map():
    coupling_list = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5]]
    cmap = CouplingMap(couplinglist=coupling_list)
    cmap.add_edge(5, 6)
    cmap.add_physical_qubit(7)
    return cmap


Test:
from qiskit.transpiler import CouplingMap
def check(candidate):
    cmap = candidate()
    edges = set(cmap.get_edges())
    assert edges == { (0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5,6) }
    assert len(cmap.physical_qubits) == 8

check(create_and_modify_coupling_map)
Create a Target object for a 2-qubit system and add UGate and CXGate instructions with specific properties.
- Add UGate for both qubits (0 and 1) with parameters 'theta', 'phi', and 'lambda'.
- Add CXGate for qubit pairs (0,1) and (1,0).
- All instructions should have nonzero 'duration' and 'error' properties set.
You must implement this using a function named `create_target` with no arguments.

Solution:
from qiskit.transpiler import Target, InstructionProperties
from qiskit.circuit.library import UGate, CXGate
from qiskit.circuit import Parameter

def create_target():
    gmap = Target()
    theta, phi, lam = [Parameter(p) for p in ("theta", "phi", "lambda")]
    u_props = {
        (0,): InstructionProperties(duration=5.23e-8, error=0.00038115),
        (1,): InstructionProperties(duration=4.52e-8, error=0.00032115),
    }
    gmap.add_instruction(UGate(theta, phi, lam), u_props)
    cx_props = {
        (0,1): InstructionProperties(duration=5.23e-7, error=0.00098115),
        (1,0): InstructionProperties(duration=4.52e-7, error=0.00132115),
    }
    gmap.add_instruction(CXGate(), cx_props)
    return gmap


Test:
from qiskit.transpiler import Target, InstructionProperties
from qiskit.circuit.library import UGate, CXGate
from qiskit.circuit import Parameter
def check(candidate):
    target = candidate()
    assert isinstance(target, Target)

    instructions = target.instructions
    u_gate_instructions = [inst for inst in instructions if inst[0].name == "u"]
    cx_gate_instructions = [inst for inst in instructions if inst[0].name == 'cx']

    assert len(u_gate_instructions) == 2
    assert len(cx_gate_instructions) == 2

    for inst in u_gate_instructions + cx_gate_instructions:
        props = target[inst[0].name][inst[1]]
        assert isinstance(props, InstructionProperties)
        assert props.duration > 0
        assert props.error >= 0

    assert set(inst[1] for inst in u_gate_instructions) == {(0,), (1,)}
    assert set(inst[1] for inst in cx_gate_instructions) == {(0, 1), (1, 0)}

check(create_target)
Synthesize an evolution gate using MatrixExponential for a given Pauli string and time.
The Pauli string can be any combination of 'I', 'X', 'Y', and 'Z'.
Return the resulting QuantumCircuit.
You must implement this using a function named `synthesize_evolution_gate` with the following arguments: pauli_string, time.

Solution:
from qiskit.circuit.library import PauliEvolutionGate
from qiskit.synthesis import MatrixExponential
from qiskit import QuantumCircuit
from qiskit.quantum_info import Pauli, Operator
import numpy as np

def synthesize_evolution_gate(pauli_string, time):
    pauli = Pauli(pauli_string)
    evolution_gate = PauliEvolutionGate(pauli, time)
    synthesizer = MatrixExponential()
    qc = synthesizer.synthesize(evolution_gate)
    return qc


Test:
from qiskit.circuit.library import PauliEvolutionGate
from qiskit.synthesis import MatrixExponential
from qiskit import QuantumCircuit
from qiskit.quantum_info import Pauli, Operator
import numpy as np
def check(candidate):
    pauli_string = "X"
    time = 1.0
    
    qc = candidate(pauli_string, time)
    assert isinstance(qc, QuantumCircuit), "The function should return a QuantumCircuit"
    assert qc.size() > 0, "The circuit should not be empty"
    
    ideal_solution = QuantumCircuit(1)
    ideal_solution.rx(2 * time, 0)
    
    assert np.allclose(Operator(qc), Operator(ideal_solution)), "The synthesized circuit does not match the expected evolution"

check(synthesize_evolution_gate)
Decompose a 4x4 unitary using the TwoQubitBasisDecomposer with CXGate as the basis gate.
Return the resulting QuantumCircuit.
You must implement this using a function named `decompose_unitary` with the following arguments: unitary.

Solution:
from qiskit.synthesis import TwoQubitBasisDecomposer
from qiskit.quantum_info import Operator, random_unitary
from qiskit.circuit.library import CXGate
from qiskit import QuantumCircuit
import numpy as np

def decompose_unitary(unitary):
    decomposer = TwoQubitBasisDecomposer(CXGate())
    return decomposer(unitary)


Test:
from qiskit.synthesis import TwoQubitBasisDecomposer
from qiskit.quantum_info import Operator, random_unitary
from qiskit.circuit.library import CXGate
from qiskit import QuantumCircuit
import numpy as np
def check(candidate):
    unitary = random_unitary(4)
    try:
        qc = candidate(unitary)
        assert isinstance(qc, QuantumCircuit)
        assert qc.num_qubits == 2
        assert qc.size() > 0

        cx_count = sum(1 for inst in qc.data if inst.operation.name == "cx")
        assert cx_count > 0
    except (ValueError, np.linalg.LinAlgError) as e:
        raise e

check(decompose_unitary)
Create a QuantumCircuit with a C3SXGate applied to the first four qubits.
You must implement this using a function named `create_c3sx_circuit` with no arguments.

Solution:
from qiskit import QuantumCircuit
from qiskit.circuit.library import C3SXGate

def create_c3sx_circuit():
    qc = QuantumCircuit(4)
    c3sx_gate = C3SXGate()
    qc.append(c3sx_gate, [0, 1, 2, 3])
    return qc


Test:
from qiskit import QuantumCircuit
from qiskit.circuit.library import C3SXGate
def check(candidate):
    qc = candidate()
    assert isinstance(qc, QuantumCircuit)
    
    c3sx_instructions = [inst for inst in qc.data if isinstance(inst.operation, C3SXGate)]
    assert len(c3sx_instructions) == 1
    
    assert c3sx_instructions[0].qubits == tuple([qc.qubits[i] for i in range(4)])

check(create_c3sx_circuit)
Create a QuantumCircuit with a CDKMRippleCarryAdder applied to the qubits.
The kind of adder can be 'full', 'half', or 'fixed'.
You must implement this using a function named `create_ripple_carry_adder_circuit` with the following arguments: num_state_qubits, kind.

Solution:
from qiskit.circuit.library import CDKMRippleCarryAdder
from qiskit import QuantumCircuit
from qiskit.quantum_info import Operator

def create_ripple_carry_adder_circuit(num_state_qubits, kind):
    adder = CDKMRippleCarryAdder(num_state_qubits, kind)
    qc = QuantumCircuit(adder.num_qubits)
    qc.append(adder.to_instruction(), range(adder.num_qubits))
    return qc


Test:
from qiskit.circuit.library import CDKMRippleCarryAdder
from qiskit import QuantumCircuit
from qiskit.quantum_info import Operator
def check(candidate):
    qc_full = candidate(3, "full")
    assert isinstance(qc_full, QuantumCircuit), "The function should return a QuantumCircuit"
    
    op_full = Operator(qc_full)
    expected_full = Operator(CDKMRippleCarryAdder(3, "full"))
    assert op_full.equiv(expected_full), "The circuit does not match the expected CDKMRippleCarryAdder for full kind"
    qc_fixed = candidate(3, "fixed")
    assert isinstance(qc_fixed, QuantumCircuit), "The function should return a QuantumCircuit"
    
    op_fixed = Operator(qc_fixed)
    expected_fixed = Operator(CDKMRippleCarryAdder(3, "fixed"))
    assert op_fixed.equiv(expected_fixed), "The circuit does not match the expected CDKMRippleCarryAdder for fixed kind"

check(create_ripple_carry_adder_circuit)
Create a QuantumCircuit with a Diagonal gate applied to the qubits.
The diagonal elements are provided in the list 'diag'.
You must implement this using a function named `create_diagonal_circuit` with the following arguments: diag.

Solution:
from qiskit.circuit.library import Diagonal
from qiskit import QuantumCircuit
from qiskit.quantum_info import Operator

def create_diagonal_circuit(diag):
    diagonal_gate = Diagonal(diag)
    qc = QuantumCircuit(diagonal_gate.num_qubits)
    qc.append(diagonal_gate.to_instruction(), range(diagonal_gate.num_qubits))
    return qc


Test:
from qiskit.circuit.library import Diagonal
from qiskit import QuantumCircuit
from qiskit.quantum_info import Operator
def check(candidate):
    diag = [1, 1j, -1, -1j]
    qc = candidate(diag)
    assert isinstance(qc, QuantumCircuit), "The function should return a QuantumCircuit"
    
    op_circuit = Operator(qc)
    
    expected_diagonal = Diagonal(diag)
    op_expected = Operator(expected_diagonal)
    
    assert op_circuit.equiv(op_expected), "The circuit does not match the expected Diagonal gate"

check(create_diagonal_circuit)