Clifford¶

class Clifford(data, validate=True)[source]¶

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-1 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 readible 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

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

Initialize an operator object.

Attributes

`Clifford.atol`	The default absolute tolerance parameter for float comparisons.
`Clifford.destabilizer`	Return the destabilizer block of the StabilizerTable.
`Clifford.dim`	Return tuple (input_shape, output_shape).
`Clifford.num_qubits`	Return the number of qubits if a N-qubit operator or None otherwise.
`Clifford.qargs`	Return the qargs for the operator.
`Clifford.rtol`	The relative tolerance parameter for float comparisons.
`Clifford.stabilizer`	Return the stabilizer block of the StabilizerTable.
`Clifford.table`	Return StabilizerTable

Methods

`Clifford.__call__`(qargs)	Return a clone with qargs set
`Clifford.__getitem__`(key)	Return a stabilizer Pauli row
`Clifford.__mul__`(other)
`Clifford.add`(other)	Return the linear operator self + other.
`Clifford.adjoint`()	Return the conjugate transpose of the Clifford
`Clifford.compose`(other[, qargs, front])	Return the composed operator.
`Clifford.conjugate`()	Return the conjugate of the Clifford.
`Clifford.copy`()	Make a deep copy of current operator.
`Clifford.dot`(other[, qargs])	Return the right multiplied operator self * other.
`Clifford.expand`(other)	Return the tensor product operator other ⊗ self.
`Clifford.from_circuit`(circuit)	Initialize from a QuantumCircuit or Instruction.
`Clifford.from_dict`(obj)	Load a Clifford from a dictionary
`Clifford.from_label`(label)	Return a tensor product of single-qubit Clifford gates.
`Clifford.input_dims`([qargs])	Return tuple of input dimension for specified subsystems.
`Clifford.is_unitary`()	Return True if the Clifford table is valid.
`Clifford.multiply`(other)	Return the linear operator other * self.
`Clifford.output_dims`([qargs])	Return tuple of output dimension for specified subsystems.
`Clifford.power`(n)	Return the compose of a operator with itself n times.
`Clifford.reshape`([input_dims, output_dims])	Return a shallow copy with reshaped input and output subsystem dimensions.
`Clifford.set_atol`(value)	Set the class default absolute tolerance parameter for float comparisons.
`Clifford.set_rtol`(value)	Set the class default relative tolerance parameter for float comparisons.
`Clifford.subtract`(other)	Return the linear operator self - other.
`Clifford.tensor`(other)	Return the tensor product operator self ⊗ other.
`Clifford.to_circuit`()	Return a QuantumCircuit implementing the Clifford.
`Clifford.to_dict`()	Return dictionary represenation of Clifford object.
`Clifford.to_instruction`()	Return a Gate instruction implementing the Clifford.
`Clifford.to_matrix`()	Convert operator to Numpy matrix.
`Clifford.to_operator`()	Convert to an Operator object.
`Clifford.transpose`()	Return the transpose of the Clifford.
`Clifford.__call__`(qargs)	Return a clone with qargs set
`Clifford.__mul__`(other)