Clifford¶

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

Bases: BaseOperator, AdjointMixin, Operation

An N-qubit unitary operator from the Clifford group.

Representation

An N-qubit Clifford operator is stored as a length 2N × (2N+1) boolean tableau 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 boolean tableau for the Clifford can be accessed using the tableau attribute. The destabilizer or stabilizer rows can each be accessed as a length-N Stabilizer table using destab and stab 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.to_labels(mode="D"))

# Print the Clifford stabilizer rows
print(cliff.to_labels(mode="S"))

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

Circuit Conversion

Clifford operators can be initialized from circuits containing only the following Clifford gates: IGate, XGate, YGate, ZGate, HGate, SGate, SdgGate, SXGate, SXdgGate, CXGate, CZGate, CYGate, DXGate, SwapGate, iSwapGate, ECRGate. 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.

Nota

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.

Referencias

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_labels`	Convert a Clifford to a list Pauli (de)stabilizer string labels.
`to_matrix`	Convert operator to Numpy matrix.
`to_operator`	Convert to an Operator object.
`transpose`	Return the transpose of the Clifford.

Attributes

destab¶: The destabilizer array for the symplectic representation.

destab_phase¶: Return phase of destaibilizer with boolean representation.

destab_x¶: The destabilizer x array for the symplectic representation.

destab_z¶: The destabilizer z array for the symplectic representation.

destabilizer¶: Return the destabilizer block of the StabilizerTable.

dim¶: Return tuple (input_shape, output_shape).

name¶: Unique string identifier for operation type.

num_clbits¶: Number of classical bits.

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

phase¶: Return phase with boolean representation.

qargs¶: Return the qargs for the operator.

stab¶: The stabilizer array for the symplectic representation.

stab_phase¶: Return phase of stablizer with boolean representation.

stab_x¶: The stabilizer x array for the symplectic representation.

stab_z¶: The stabilizer array for the symplectic representation.

stabilizer¶: Return the stabilizer block of the StabilizerTable.

symplectic_matrix¶: Return boolean symplectic matrix.

table¶: Return StabilizerTable

x¶: The x array for the symplectic representation.

z¶: The z array for the symplectic representation.