Quantum Gates

Quantum gate reference for PennyLane, Qiskit, and OpenQASM on Dynex

Quantum Gates on Dynex

Quantum gates are the building blocks of quantum circuits. Each gate performs a specific unitary operation on one or more qubits, altering their probability amplitudes and phases. Dynex supports all standard gates via PennyLane, Qiskit, and OpenQASM.

Single-Qubit Gates

Pauli-X (NOT gate)

Flips the qubit state: X|0⟩ = |1⟩, X|1⟩ = |0⟩.

Framework	Syntax
PennyLane	qml.PauliX(wires=0)
OpenQASM	x q[0];
Qiskit	qc.x(0)

Pauli-Y

Phase flip then bit flip: Y|0⟩ = i|1⟩, Y|1⟩ = −i|0⟩.

Framework	Syntax
PennyLane	qml.PauliY(wires=0)
OpenQASM	y q[0];
Qiskit	qc.y(0)

Pauli-Z

Phase flip: Z|0⟩ = |0⟩, Z|1⟩ = −|1⟩.

Framework	Syntax
PennyLane	qml.PauliZ(wires=0)
OpenQASM	z q[0];
Qiskit	qc.z(0)

Hadamard (H)

Creates equal superposition: H|0⟩ = (|0⟩ + |1⟩)/√2.

Framework	Syntax
PennyLane	qml.Hadamard(wires=0)
OpenQASM	h q[0];
Qiskit	qc.h(0)

T Gate

Applies a π/4 phase shift. Non-Clifford gate essential for universal quantum computation.

Framework	Syntax
PennyLane	qml.T(wires=0)
OpenQASM	t q[0];
Qiskit	qc.t(0)

Rotation Gates

RX, RY, RZ

Single-axis rotations by angle θ.

Gate	PennyLane	Qiskit
RX	qml.RX(theta, wires=0)	qc.rx(theta, 0)
RY	qml.RY(theta, wires=0)	qc.ry(theta, 0)
RZ	qml.RZ(theta, wires=0)	qc.rz(theta, 0)

Two-Qubit Gates

CNOT (CX)

Flips target qubit if control qubit is |1⟩.

Framework	Syntax
PennyLane	qml.CNOT(wires=[0, 1])
OpenQASM	cx q[0], q[1];
Qiskit	qc.cx(0, 1)

Controlled-Z (CZ)

Applies Z to target if control is |1⟩.

Framework	Syntax
PennyLane	qml.CZ(wires=[0, 1])
OpenQASM	cz q[0], q[1];
Qiskit	qc.cz(0, 1)

SWAP (Fredkin)

Exchanges the states of two qubits.

Framework	Syntax
PennyLane	qml.SWAP(wires=[0, 1])
OpenQASM	swap q[0], q[1];
Qiskit	qc.swap(0, 1)

Controlled Rotations (CRX, CRY, CRZ)

Apply rotation to target qubit if control is |1⟩.

Gate	PennyLane	Qiskit
CRX	qml.CRX(theta, wires=[0, 1])	qc.crx(theta, 0, 1)
CRY	qml.CRY(theta, wires=[0, 1])	qc.cry(theta, 0, 1)
CRZ	qml.CRZ(theta, wires=[0, 1])	qc.crz(theta, 0, 1)

Controlled Phase Shift

Applies phase shift to target if control is |1⟩.

Framework	Syntax
PennyLane	qml.ControlledPhaseShift(theta, wires=[0, 1])
Qiskit	qc.cp(theta, 0, 1)

Three-Qubit Gates

Toffoli (CCNOT)

Flips target if both control qubits are |1⟩.

Framework	Syntax
PennyLane	qml.Toffoli(wires=[0, 1, 2])
OpenQASM	ccx q[0], q[1], q[2];
Qiskit	qc.ccx(0, 1, 2)

Advanced Operations

Quantum Fourier Transform (QFT)

# PennyLane
def qft(wires):
    qml.QFT(wires=wires)

# Qiskit
from qiskit.circuit.library import QFT
qc.append(QFT(num_qubits).decompose(), range(num_qubits))

Adjoint (Dagger)

# PennyLane
qml.adjoint(qml.Hadamard)(wires=0)

# Qiskit
qc.h(0).inverse()

Basis Embedding

Encodes classical binary data into quantum states:

# PennyLane
qml.BasisEmbedding(features, wires=[0, 1, 2])

Controlled Unitary (CU)

# PennyLane
qml.ControlledQubitUnitary(U_matrix, control_wires=[0], wires=[1])

Next: Running circuits on Dynex

See DynexCircuit Class to learn how to execute these gates on the Dynex platform.