Section1: Perform Quantum Computing - Qiskit v2.X developer certification exam prep

TASK1.1: Define Pauli Operators¶

In quantum computing, a Pauli operation refers to applying one of the three Pauli matrices—X, Y, or Z—to a qubit.

X (Pauli-X): Bit-flip (like a classical NOT gate).
Z (Pauli-Z): Phase-flip (adds a relative phase of −1 to $|1⟩$ ).
Y (Pauli-Y): Combination of bit-flip and phase-flip.

X = \sigma_x = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}, \quad Y = \sigma_y = \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix}, \quad Z = \sigma_z = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}

(1)

Which matrix is generated by the following code?

from qiskit.quantum_info import Pauli
p = Pauli("XZ")
print(p.to_matrix())

a. $\begin{bmatrix}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & -1 \\ 0 & 0 & -1 & 0 \end{bmatrix}$

b. $\begin{bmatrix}0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \\ 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \end{bmatrix}$

c. $\begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \end{bmatrix}$

d. $\begin{bmatrix}0 & -i & 0 & 0 \\ i & 0 & 0 & 0 \\ 0 & 0 & 0 & i \\ 0 & 0 & -i & 0 \end{bmatrix}$

Answer: a

The label "XZ" corresponds to the tensor product $X \otimes Z$ . The to_matrix() method constructs the full matrix representation. Option (a) matches this result, as it applies $X$ on the first qubit and $Z$ on the second qubit.

from qiskit.quantum_info import Pauli
p = Pauli("XZ")
print(p.to_matrix())

[[ 0.+0.j  0.+0.j  1.+0.j  0.+0.j]
 [ 0.+0.j  0.+0.j  0.+0.j -1.+0.j]
 [ 1.+0.j  0.+0.j  0.+0.j  0.+0.j]
 [ 0.+0.j -1.+0.j  0.+0.j  0.+0.j]]

Which of the following input formats are valid when creating a Pauli object?

a. Pauli("IXYZ")
b. Pauli([1, 0, 1, 1])
c. Pauli((z_bits, x_bits))
d. Pauli(np.array([[0, 1],[1, 0]]))

What label is printed by the following code?

from qiskit.quantum_info import Pauli
p = Pauli("XZ")
q = Pauli("ZI")
r = p.compose(q)
print(r.to_label())

a. "YZ"
b. "iZZ"
c. "XI"
d. "iYZ"

Answer: d

When composing Pauli("XZ") with Pauli("ZI"), the operation corresponds to matrix multiplication in the correct qubit order. The compose() method applies the second Pauli on the right, consistent with operator composition.

from qiskit.quantum_info import Pauli
p = Pauli("XZ")
q = Pauli("ZI")
r = p.compose(q)
print(r.to_label())

iYZ

Which of the following best describes the role of the dot() method in the Pauli class?

a. Multiplies two Pauli operators and returns a new Pauli
b. Converts the Pauli to a matrix and computes the inner product
c. Combines two Pauli operators by tensor product
d. Generates the Hamiltonian representation of a Pauli operator

Answer: a

Composition compose() by default is defined as left matrix multiplication, while dot() is defined as right matrix multiplication.
Setting the front=True kwarg changes this to right multiplication and is equivalent to the dot() method: A.dot(B) == A.compose(B, front=True)

from qiskit.quantum_info import Pauli
p = Pauli("X")
q = Pauli("Z")
r = p.dot(q)
print(r.to_label())

-iY

TASK 1.2: Apply quantum operations¶

Which method appends one or more instructions to the end of the circuit, modifying the circuit in place?

a. compose
b. append
c. to_instruction
d. decompose

By default, what does QuantumCircuit.compose(other) return when called without inplace=True?

a. It mutates the left-hand circuit and returns None.
b. It returns a new combined circuit.
c. It mutates the right-hand circuit and returns it.
d. It raises an error unless inplace is specified.

The answer is b.

By default, compose returns a new circuit object that represents the composition, leaving the original circuit unchanged unless inplace=True is specified.

from qiskit import QuantumCircuit

left = QuantumCircuit(1, name="left")
left.h(0)

right = QuantumCircuit(1, name="right")
right.x(0)

# 1) default（inplace=False）
combined = left.compose(right)   # ← new circuit
print("left unchanged:\n", left.draw())
print("right unchanged:\n", right.draw())
print("combined (left then right):\n", combined.draw())

# inplace=True
left2 = QuantumCircuit(1, name="left2")
left2.h(0)

ret = left2.compose(right, inplace=True)
print("left2 mutated:\n", left2.draw())
print("ret is left2?:", ret is left2)

left unchanged:
    ┌───┐
q: ┤ H ├
   └───┘
right unchanged:
    ┌───┐
q: ┤ X ├
   └───┘
combined (left then right):
    ┌───┐┌───┐
q: ┤ H ├┤ X ├
   └───┘└───┘
left2 mutated:
    ┌───┐┌───┐
q: ┤ H ├┤ X ├
   └───┘└───┘
ret is left2?: False

Which code correctly composes qc_b onto qc_a so that qc_b’s qubits (0, 1) map to qc_a’s qubits (1, 3), without mutating qc_a?

a. qc_a.compose(qc_b, qubits=[1, 3])
b. qc_a.compose(qc_b, [1, 3], inplace=True)
c. qc_a.append(qc_b, [1, 3])
d. qc_b.compose(qc_a, qubits=[1, 3])

Which snippet converts a subcircuit to an instruction and appends it to another circuit?

a.

inst = qc_b.to_instruction()
qc_a.append(inst, [1, 3])

b.

inst = qc_b.to_gate()
qc_a.compose(inst, [1, 3])

c.

inst = qc_b.compose()
qc_a.append(inst, [1, 3])

d.

inst = qc_b.control()
qc_a.append(inst, [1, 3])

Select all that apply: Which statements about turning circuits into reusable operations are correct?

a. to_gate() requires the source circuit to be unitary.
b. A Gate produced by to_gate() can be made controlled via .control().
c. to_instruction() returns a Gate.
d. to_gate() always mutates the original circuit.

What happens if you call qc.barrier() with no qubit arguments?

a. It inserts no operation.
b. It raises an error.
c. It applies a barrier to all qubits in the circuit.
d. It applies a barrier only to measured qubits.

Which statement about decompose() on a circuit is correct?

a. It mutates the circuit to expand each instruction into its definition.
b. It returns a new circuit with instructions expanded into their definitions.
c. It removes all non-unitary operations from the circuit.
d. It only affects instructions with labels.

The QuantumCircuit.data attribute is best described as which of the following?

a. A list of Instruction objects only.
b. A list of CircuitInstruction objects, each with an operation and its qubits/clbits.
c. A tuple of (operation, parameters) pairs.
d. A dictionary keyed by gate names.

The answer is b.

QuantumCircuit.data is a list of CircuitInstruction objects. Each contains an operation along with the associated quantum and classical arguments (qubits, clbits).

from qiskit.circuit import QuantumCircuit
qc = QuantumCircuit(1)
qc.x(0)
print(qc.data)

[CircuitInstruction(operation=Instruction(name='x', num_qubits=1, num_clbits=0, params=[]), qubits=(<Qubit register=(1, "q"), index=0>,), clbits=())]

Which call correctly applies a custom 4×4 unitary matrix U to qubits [0, 1] with label "U"?

a. qc.unitary(U, [0, 1], label="U")
b. qc.append(U, [0, 1], label="U")
c. qc.compose(U, [0, 1], inplace=True)
d. qc.to_gate(U, [0, 1], label="U")

Which method applies a multiple-controlled Z-axis rotation of angle lam with control qubits in controls and target t?

a. qc.mcrx(lam, controls, t)
b. qc.mcry(lam, controls, t)
c. qc.mcrz(lam, controls, t)
d. qc.crz(lam, controls, t)

Which statement about append and CircuitInstruction is correct?

a. When passing a CircuitInstruction to append, you must also pass qargs and cargs.
b. Passing a CircuitInstruction to append forbids also passing separate qargs or cargs.
c. append cannot accept CircuitInstruction objects.
d. append never returns a handle to the added instruction(s).

Which snippet uses the circuit library to append a single-qubit H operation to qubit 0?

a. qc.append(HGate(), [0])
b. qc.compose(HGate(), [0])
c. qc.to_instruction(HGate(), [0])
d. qc.control(HGate(), [0])

You have built a two-qubit subcircuit qc_b and wish to create a controlled version of it with one control and two targets. Which sequence achieves this before appending to qc_a?

a.

gate = qc_b.to_gate().control()
qc_a.append(gate, [c, t0, t1])

b.

gate = qc_b.to_instruction().control()
qc_a.append(gate, [c, t0, t1])

c.

gate = qc_b.compose().control()
qc_a.append(gate, [c, t0, t1])

d.

gate = qc_b.control()
qc_a.append(gate, [c, t0, t1])

Which statement about qubit remapping when composing circuits is correct?

a. compose does not support remapping; qubits must match by index.
b. You can specify a list of target qubit indices via the qubits argument.
c. Remapping is only available with append, not compose.
d. Remapping requires both circuits to have the same number of classical bits.

Select all that apply: Which methods can convert a circuit into a reusable operation that can be inserted into other circuits?

a. to_instruction()
b. to_gate()
c. decompose()
d. append()

Which method returns the number of layers of quantum gates that must be executed sequentially in a circuit?

a. size()
b. depth()
c. count_ops()
d. width()

What is a key conceptual difference between an Instruction and a QuantumCircuit in Qiskit?

a. Instructions are immutable, while circuits are typically mutable.
b. Circuits can only contain unitary operations, while instructions can include non-unitary ones.
c. Instructions support barriers, while circuits do not.
d. Circuits are immutable, while instructions are mutable.

Which statement about parameterized circuits in Qiskit is correct?

a. Parameters must be defined with numerical values at circuit creation time.
b. Undefined parameters can be assigned values later using assign_parameters().
c. The parameters attribute of a circuit always returns an empty list.
d. Parameterized circuits cannot be transpiled.

Which object type is used to represent a symbolic parameter in a Qiskit circuit?

a. ParameterView
b. ParameterExpression
c. Parameter
d. SymbolicVariable

Why are parameterized circuits useful in variational algorithms?

a. They reduce the number of qubits required by an algorithm.
b. They allow constructing and transpiling the circuit once, while reusing it with different parameter values.
c. They automatically parallelize parameter updates across multiple backends.
d. They eliminate the need for classical optimizers.