qiskit.quantum_info.Clifford
class Clifford(data, validate=True)
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 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.
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.
__init__
__init__(data, validate=True)
Initialize an operator object.
Methods
__init__(data[, validate]) | Initialize an operator object. |
add(other) | Return the linear operator self + other. |
adjoint() | Return the conjugate transpose of the Clifford |
compose(other[, qargs, front]) | Return the composed operator. |
conjugate() | Return the conjugate of the Clifford. |
copy() | Make a deep copy of current operator. |
dot(other[, qargs]) | Return the right multiplied operator self * other. |
expand(other) | Return the tensor product operator other ⊗ self. |
from_circuit(circuit) | Initialize from a QuantumCircuit or Instruction. |
from_dict(obj) | Load a Clifford from a dictionary |
from_label(label) | Return a tensor product of single-qubit Clifford gates. |
input_dims([qargs]) | Return tuple of input dimension for specified subsystems. |
is_unitary() | Return True if the Clifford table is valid. |
multiply(other) | Return the linear operator other * self. |
output_dims([qargs]) | Return tuple of output dimension for specified subsystems. |
power(n) | Return the compose of a operator with itself n times. |
reshape([input_dims, output_dims]) | Return a shallow copy with reshaped input and output subsystem dimensions. |
set_atol(value) | Set the class default absolute tolerance parameter for float comparisons. |
set_rtol(value) | Set the class default relative tolerance parameter for float comparisons. |
subtract(other) | Return the linear operator self - other. |
tensor(other) | Return the tensor product operator self ⊗ other. |
to_circuit() | Return a QuantumCircuit implementing the Clifford. |
to_dict() | Return dictionary represenation 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
atol | The default absolute tolerance parameter for float comparisons. |
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. |
rtol | The relative tolerance parameter for float comparisons. |
stabilizer | Return the stabilizer block of the StabilizerTable. |
table | Return StabilizerTable |
add
add(other)
Return the linear operator self + other.
DEPRECATED: use operator + other instead.
Parameters
other (BaseOperator) – an operator object.
Returns
the operator self + other.
Return type
BaseOperator
adjoint
adjoint()
Return the conjugate transpose of the Clifford
atol
The default absolute tolerance parameter for float comparisons.
compose
compose(other, qargs=None, front=False)
Return the composed operator.
Parameters
- other (Clifford) – an operator object.
- qargs (list or None) – a list of subsystem positions to apply other on. If None apply on all subsystems [default: None].
- front (bool) – If True compose using right operator multiplication, instead of left multiplication [default: False].
Returns
The operator self @ other.
Return type
Raises
QiskitError – if operators have incompatible dimensions for composition.
Additional Information:
Composition (@) is defined as left matrix multiplication for matrix operators. That is that A @ B is equal to B * A. Setting front=True returns right matrix multiplication A * B and is equivalent to the dot() method.
conjugate
conjugate()
Return the conjugate of the Clifford.
copy
copy()
Make a deep copy of current operator.
destabilizer
Return the destabilizer block of the StabilizerTable.
dim
Return tuple (input_shape, output_shape).
dot
dot(other, qargs=None)
Return the right multiplied operator self * other.
Parameters
- other (Clifford) – an operator object.
- qargs (list or None) – a list of subsystem positions to apply other on. If None apply on all subsystems [default: None].
Returns
The operator self * other.
Return type
Raises
QiskitError – if operators have incompatible dimensions for composition.
expand
expand(other)
Return the tensor product operator other ⊗ self.
Parameters
other (Clifford) – an operator object.
Returns
the tensor product operator other ⊗ self.
Return type
from_circuit
static from_circuit(circuit)
Initialize from a QuantumCircuit or Instruction.
Parameters
circuit (QuantumCircuit orInstruction) – instruction to initialize.
Returns
the Clifford object for the instruction.
Return type
Raises
QiskitError – if the input instruction is non-Clifford or contains classical register instruction.
from_dict
static from_dict(obj)
Load a Clifford from a dictionary
from_label
static from_label(label)
Return a tensor product of single-qubit Clifford gates.
Parameters
label (string) – single-qubit operator string.
Returns
The N-qubit Clifford operator.
Return type
Raises
QiskitError – if the label contains invalid characters.
Additional Information:
The labels correspond to the single-qubit Cliffords are
-
- Label
- Stabilizer
- Destabilizer
-
"I"- +Z
- +X
-
"X"- -Z
- +X
-
"Y"- -Z
- -X
-
"Z"- +Z
- -X
-
"H"- +X
- +Z
-
"S"- +Z
- +Y
input_dims
input_dims(qargs=None)
Return tuple of input dimension for specified subsystems.
is_unitary
is_unitary()
Return True if the Clifford table is valid.
multiply
multiply(other)
Return the linear operator other * self.
DEPRECATED: use other * operator instead.
Parameters
other (complex) – a complex number.
Returns
the linear operator other * self.
Return type
BaseOperator
Raises
NotImplementedError – if subclass does not support multiplication.
num_qubits
Return the number of qubits if a N-qubit operator or None otherwise.
output_dims
output_dims(qargs=None)
Return tuple of output dimension for specified subsystems.
power
power(n)
Return the compose of a operator with itself n times.
Parameters
n (int) – the number of times to compose with self (n>0).
Returns
the n-times composed operator.
Return type
BaseOperator
Raises
QiskitError – if the input and output dimensions of the operator are not equal, or the power is not a positive integer.
qargs
Return the qargs for the operator.
reshape
reshape(input_dims=None, output_dims=None)
Return a shallow copy with reshaped input and output subsystem dimensions.
Arg:
input_dims (None or tuple): new subsystem input dimensions.
If None the original input dims will be preserved [Default: None].
output_dims (None or tuple): new subsystem output dimensions.
If None the original output dims will be preserved [Default: None].
Returns
returns self with reshaped input and output dimensions.
Return type
BaseOperator
Raises
QiskitError – if combined size of all subsystem input dimension or subsystem output dimensions is not constant.
rtol
The relative tolerance parameter for float comparisons.
set_atol
classmethod set_atol(value)
Set the class default absolute tolerance parameter for float comparisons.
DEPRECATED: use operator.atol = value instead
set_rtol
classmethod set_rtol(value)
Set the class default relative tolerance parameter for float comparisons.
DEPRECATED: use operator.rtol = value instead
stabilizer
Return the stabilizer block of the StabilizerTable.
subtract
subtract(other)
Return the linear operator self - other.
DEPRECATED: use operator - other instead.
Parameters
other (BaseOperator) – an operator object.
Returns
the operator self - other.
Return type
BaseOperator
table
Return StabilizerTable
tensor
tensor(other)
Return the tensor product operator self ⊗ other.
Parameters
other (Clifford) – a operator subclass object.
Returns
the tensor product operator self ⊗ other.
Return type
to_circuit
to_circuit()
Return a QuantumCircuit implementing the Clifford.
For N <= 3 qubits this is based on optimal CX cost decomposition from reference [1]. For N > 3 qubits this is done using the general non-optimal compilation routine from reference [2].
Returns
a circuit implementation of the Clifford.
Return type
References
- S. Bravyi, D. Maslov, Hadamard-free circuits expose the structure of the Clifford group, arXiv:2003.09412 [quant-ph]
- S. Aaronson, D. Gottesman, Improved Simulation of Stabilizer Circuits, Phys. Rev. A 70, 052328 (2004). arXiv:quant-ph/0406196
to_dict
to_dict()
Return dictionary represenation of Clifford object.
to_instruction
to_instruction()
Return a Gate instruction implementing the Clifford.
to_matrix
to_matrix()
Convert operator to Numpy matrix.
to_operator
to_operator()
Convert to an Operator object.
transpose
transpose()
Return the transpose of the Clifford.