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Clifford

class Clifford(data, validate=True)[código fonte]

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, 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.

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.

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_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.