Quantum operations

PennyLane supports a wide variety of quantum operations—such as gates, noisy channels, state preparations and measurements. These operations can be used exclusively in quantum functions, like shown in the following example:

import pennylane as qml

def my_quantum_function(x, y):
    qml.RZ(x, wires=0)
    qml.CNOT(wires=[0,1])
    qml.RY(y, wires=1)
    qml.T(wires=0).inv()
    qml.AmplitudeDamping(0.1, wires=0)
    return qml.expval(qml.PauliZ(1))

This quantum function uses the RZ, CNOT, RY gates, the AmplitudeDamping noisy channel as well as the PauliZ observable.

Note that PennyLane supports inverting quantum operations via the Op(param, wires).inv() method. Additionally, PennyLane provides a function qml.inv that can be used to invert sequences of operations and Templates.

Below is a list of all quantum operations supported by PennyLane.

Qubit operations

Qubit gates

Hadamard	The Hadamard operator
PauliX	The Pauli X operator
PauliY	The Pauli Y operator
PauliZ	The Pauli Z operator
S	The single-qubit phase gate
T	The single-qubit T gate
SX	The single-qubit Square-Root X operator.
Rot	Arbitrary single qubit rotation
RX	The single qubit X rotation
RY	The single qubit Y rotation
RZ	The single qubit Z rotation
MultiRZ	Arbitrary multi Z rotation.
PauliRot	Arbitrary Pauli word rotation.
PhaseShift	Arbitrary single qubit local phase shift
CNOT	The controlled-NOT operator
CZ	The controlled-Z operator
CY	The controlled-Y operator
SWAP	The swap operator
U1	U1 gate.
U2	U2 gate.
U3	Arbitrary single qubit unitary.
CRot	The controlled-Rot operator
CRX	The controlled-RX operator
CRY	The controlled-RY operator
CRZ	The controlled-RZ operator
Toffoli	Toffoli (controlled-controlled-X) gate.
CSWAP	The controlled-swap operator
QubitUnitary	Apply an arbitrary fixed unitary matrix.
DiagonalQubitUnitary	Apply an arbitrary fixed diagonal unitary matrix.

Qubit state preparation

BasisState	Prepares a single computational basis state.
QubitStateVector	Prepare subsystems using the given ket vector in the computational basis.

Noisy channels

AmplitudeDamping	Single-qubit amplitude damping error channel.
GeneralizedAmplitudeDamping	Single-qubit generalized amplitude damping error channel.
PhaseDamping	Single-qubit phase damping error channel.
DepolarizingChannel	Single-qubit symmetrically depolarizing error channel.
BitFlip	Single-qubit bit flip (Pauli \(X\)) error channel.
PhaseFlip	Single-qubit bit flip (Pauli \(Z\)) error channel.
QubitChannel	Apply an arbitrary fixed quantum channel.

Qubit observables

Hadamard	The Hadamard operator
Hermitian	An arbitrary Hermitian observable.
PauliX	The Pauli X operator
PauliY	The Pauli Y operator
PauliZ	The Pauli Z operator

Grouping Pauli words

Grouping Pauli words can be used for the optimizing the measurement of qubit Hamiltonians. Along with groups of observables, post-measurement rotations can also be obtained using optimize_measurements():

>>> obs = [qml.PauliY(0), qml.PauliX(0) @ qml.PauliX(1), qml.PauliZ(1)]
>>> coeffs = [1.43, 4.21, 0.97]
>>> post_rotations, diagonalized_groupings, grouped_coeffs = optimize_measurements(obs, coeffs)
>>> post_rotations
[[RY(-1.5707963267948966, wires=[0]), RY(-1.5707963267948966, wires=[1])],
 [RX(1.5707963267948966, wires=[0])]]

The post-measurement rotations can be used to diagonalize the partitions of observables found.

For further details on measurement optimization, grouping observables through solving the minimum clique cover problem, and auxiliary functions, refer to the qml.grouping subpackage.

Continuous-variable (CV) operations

CV Gates

Beamsplitter	Beamsplitter interaction.
ControlledAddition	Controlled addition operation.
ControlledPhase	Controlled phase operation.
CrossKerr	Cross-Kerr interaction.
CubicPhase	Cubic phase shift.
Displacement	Phase space displacement.
Interferometer	A linear interferometer transforming the bosonic operators according to the unitary matrix \(U\).
Kerr	Kerr interaction.
QuadraticPhase	Quadratic phase shift.
Rotation	Phase space rotation.
Squeezing	Phase space squeezing.
TwoModeSqueezing	Phase space two-mode squeezing.

CV state preparation

CatState	Prepares a cat state.
CoherentState	Prepares a coherent state.
DisplacedSqueezedState	Prepares a displaced squeezed vacuum state.
FockDensityMatrix	Prepare subsystems using the given density matrix in the Fock basis.
FockState	Prepares a single Fock state.
FockStateVector	Prepare subsystems using the given ket vector in the Fock basis.
GaussianState	Prepare subsystems in a given Gaussian state.
SqueezedState	Prepares a squeezed vacuum state.
ThermalState	Prepares a thermal state.

CV observables

FockStateProjector	The number state observable \(\ket{n}\bra{n}\).
NumberOperator	The photon number observable \(\langle \hat{n}\rangle\).
TensorN	The tensor product of the NumberOperator acting on different wires.
P	The momentum quadrature observable \(\hat{p}\).
PolyXP	An arbitrary second-order polynomial observable.
QuadOperator	The generalized quadrature observable \(\x_\phi = \x cos\phi+\p\sin\phi\).
X	The position quadrature observable \(\hat{x}\).

Shared operations

The only operation shared by both qubit and continouous-variable architectures is the Identity.

Identity

The identity observable \(\I\).