Clifford

class Clifford(data, validate=True)

Bases: qiskit.quantum_info.operators.base_operator.BaseOperator, qiskit.quantum_info.operators.mixins.adjoint.AdjointMixin

An N-qubit unitary operator from the Clifford group.

Representation

An N-qubit Clifford operator is stored as a length 2N StabilizerTable using the convention from reference [1].

• Rows 0 to N-1 are the destabilizer group generators

• Rows N to 2N-1 are the stabilizer group generators.

The internal StabilizerTable for the Clifford can be accessed using the table attribute. The destabilizer or stabilizer rows can each be accessed as a length-N Stabilizer table using destabilizer and stabilizer attributes.

A more easily human readable representation of the Clifford operator can be obtained by calling the to_dict() method. This representation is also used if a Clifford object is printed as in the following example

from qiskit import QuantumCircuit
from qiskit.quantum_info import Clifford

# Bell state generation circuit
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
cliff = Clifford(qc)

# Print the Clifford
print(cliff)

# Print the Clifford destabilizer rows
print(cliff.destabilizer)

# Print the Clifford stabilizer rows
print(cliff.stabilizer)

Clifford: Stabilizer = ['+XX', '+ZZ'], Destabilizer = ['+IZ', '+XI']
StabilizerTable: ['+IZ', '+XI']
StabilizerTable: ['+XX', '+ZZ']

Circuit Conversion

Clifford operators can be initialized from circuits containing only the following Clifford gates: IGate, XGate, YGate, ZGate, HGate, SGate, SdgGate, CXGate, CZGate, SwapGate. They can be converted back into a QuantumCircuit, or Gate object using the to_circuit() or to_instruction() methods respectively. Note that this decomposition is not necessarily optimal in terms of number of gates.

Note

A minimally generating set of gates for Clifford circuits is the HGate and SGate gate and either the CXGate or CZGate two-qubit gate.

Clifford operators can also be converted to Operator objects using the to_operator() method. This is done via decomposing to a circuit, and then simulating the circuit as a unitary operator.

References

1. S. Aaronson, D. Gottesman, Improved Simulation of Stabilizer Circuits, Phys. Rev. A 70, 052328 (2004). arXiv:quant-ph/0406196

Initialize an operator object.

Methods

adjoint	Return the adjoint of the Operator.
compose	Return the operator composition with another Clifford.
conjugate	Return the conjugate of the Clifford.
copy	Make a deep copy of current operator.
dot	Return the right multiplied operator self * other.
expand	Return the reverse-order tensor product with another Clifford.
from_circuit	Initialize from a QuantumCircuit or Instruction.
from_dict	Load a Clifford from a dictionary
from_label	Return a tensor product of single-qubit Clifford gates.
input_dims	Return tuple of input dimension for specified subsystems.
is_unitary	Return True if the Clifford table is valid.
output_dims	Return tuple of output dimension for specified subsystems.
power	Return the compose of a operator with itself n times.
reshape	Return a shallow copy with reshaped input and output subsystem dimensions.
tensor	Return the tensor product with another Clifford.
to_circuit	Return a QuantumCircuit implementing the Clifford.
to_dict	Return dictionary representation of Clifford object.
to_instruction	Return a Gate instruction implementing the Clifford.
to_matrix	Convert operator to Numpy matrix.
to_operator	Convert to an Operator object.
transpose	Return the transpose of the Clifford.

Attributes

destabilizer

Return the destabilizer block of the StabilizerTable.

dim

Return tuple (input_shape, output_shape).

num_qubits

Return the number of qubits if a N-qubit operator or None otherwise.

qargs

Return the qargs for the operator.

settings

Return operator settings.

stabilizer

Return the stabilizer block of the StabilizerTable.

table

Return StabilizerTable