316 lines
10 KiB
Plaintext
316 lines
10 KiB
Plaintext
---
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title: CNOTDihedral
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description: API reference for qiskit.ignis.verification.CNOTDihedral
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.ignis.verification.CNOTDihedral
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---
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# CNOTDihedral
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<Class id="qiskit.ignis.verification.CNOTDihedral" isDedicatedPage={true} github="https://github.com/qiskit-community/qiskit-ignis/tree/stable/0.6/qiskit/ignis/verification/randomized_benchmarking/dihedral.py" signature="CNOTDihedral(data, validate=True)" modifiers="class">
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Bases: `qiskit.quantum_info.operators.base_operator.BaseOperator`
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CNOT-dihedral Object Class. The CNOT-dihedral group on num\_qubits qubits is generated by the gates CNOT, T and X.
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**References**
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1. Shelly Garion and Andrew W. Cross, *On the structure of the CNOT-Dihedral group*, [arXiv:2006.12042 \[quant-ph\]](https://arxiv.org/abs/2006.12042)
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2. Andrew W. Cross, Easwar Magesan, Lev S. Bishop, John A. Smolin and Jay M. Gambetta, *Scalable randomised benchmarking of non-Clifford gates*, npj Quantum Inf 2, 16012 (2016).
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Initialize a CNOTDihedral operator object.
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## Methods
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### adjoint
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<Function id="qiskit.ignis.verification.CNOTDihedral.adjoint" signature="CNOTDihedral.adjoint()">
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Return the conjugate transpose of the CNOTDihedral element
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</Function>
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### cnot
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<Function id="qiskit.ignis.verification.CNOTDihedral.cnot" signature="CNOTDihedral.cnot(i, j)">
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Apply a CNOT gate to this element. Left multiply the element by CNOT\_\{i,j}.
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</Function>
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### compose
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<Function id="qiskit.ignis.verification.CNOTDihedral.compose" signature="CNOTDihedral.compose(other, qargs=None, front=False)">
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Return the composed operator.
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**Parameters**
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* **other** ([*CNOTDihedral*](qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")) – an operator object.
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* **qargs** (*None*) – using specific qargs is not implemented for this operator.
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* **front** (*bool*) – if True compose using right operator multiplication, instead of left multiplication \[default: False].
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**Returns**
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The operator self @ other.
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**Return type**
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[CNOTDihedral](qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")
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**Raises**
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* **QiskitError** – if operators have incompatible dimensions for composition.
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* **NotImplementedError** – if qargs is not None.
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#### Additional Information:
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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()`](qiskit.ignis.verification.CNOTDihedral#dot "qiskit.ignis.verification.CNOTDihedral.dot") method.
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</Function>
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### conjugate
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<Function id="qiskit.ignis.verification.CNOTDihedral.conjugate" signature="CNOTDihedral.conjugate()">
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Return the conjugate of the CNOTDihedral element.
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</Function>
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### copy
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<Function id="qiskit.ignis.verification.CNOTDihedral.copy" signature="CNOTDihedral.copy()">
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Make a deep copy of current operator.
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</Function>
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### dot
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<Function id="qiskit.ignis.verification.CNOTDihedral.dot" signature="CNOTDihedral.dot(other, qargs=None)">
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Return the right multiplied operator self \* other.
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**Parameters**
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* **other** ([*CNOTDihedral*](qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")) – an operator object.
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* **qargs** (*None*) – using specific qargs is not implemented for this operator.
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**Returns**
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The operator self \* other.
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**Return type**
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[CNOTDihedral](qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")
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**Raises**
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* **QiskitError** – if operators have incompatible dimensions for composition.
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* **NotImplementedError** – if qargs is not None.
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</Function>
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### expand
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<Function id="qiskit.ignis.verification.CNOTDihedral.expand" signature="CNOTDihedral.expand(other)">
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Return the tensor product operator: other tensor self.
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**Parameters**
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**other** ([*CNOTDihedral*](qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")) – an operator subclass object.
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**Returns**
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the tensor product operator: other tensor other.
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**Return type**
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[CNOTDihedral](qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")
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</Function>
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### flip
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<Function id="qiskit.ignis.verification.CNOTDihedral.flip" signature="CNOTDihedral.flip(i)">
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Apply X to this element. Left multiply the element by X\_i.
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</Function>
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### from\_circuit
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<Function id="qiskit.ignis.verification.CNOTDihedral.from_circuit" signature="CNOTDihedral.from_circuit(circuit)">
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Initialize from a QuantumCircuit or Instruction.
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**Parameters**
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**circuit** ([*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") *or*[*Instruction*](qiskit.circuit.Instruction "qiskit.circuit.Instruction")) – instruction to initialize.
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**Returns**
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the CNOTDihedral object for the circuit.
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**Return type**
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[CNOTDihedral](qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")
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**Raises**
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**QiskitError** – if the input instruction is not CNOTDihedral or contains classical register instruction.
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</Function>
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### input\_dims
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<Function id="qiskit.ignis.verification.CNOTDihedral.input_dims" signature="CNOTDihedral.input_dims(qargs=None)">
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Return tuple of input dimension for specified subsystems.
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</Function>
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### is\_cnotdihedral
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<Function id="qiskit.ignis.verification.CNOTDihedral.is_cnotdihedral" signature="CNOTDihedral.is_cnotdihedral()">
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Return True if input is a CNOTDihedral element.
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</Function>
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### output\_dims
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<Function id="qiskit.ignis.verification.CNOTDihedral.output_dims" signature="CNOTDihedral.output_dims(qargs=None)">
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Return tuple of output dimension for specified subsystems.
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</Function>
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### phase
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<Function id="qiskit.ignis.verification.CNOTDihedral.phase" signature="CNOTDihedral.phase(k, i)">
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Apply an k-th power of T to this element. Left multiply the element by T\_i^k.
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</Function>
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### power
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<Function id="qiskit.ignis.verification.CNOTDihedral.power" signature="CNOTDihedral.power(n)">
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Return the compose of a operator with itself n times.
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**Parameters**
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**n** (*int*) – the number of times to compose with self (n>0).
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**Returns**
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the n-times composed operator.
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**Return type**
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[Pauli](qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli")
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**Raises**
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**QiskitError** – if the input and output dimensions of the operator are not equal, or the power is not a positive integer.
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</Function>
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### reshape
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<Function id="qiskit.ignis.verification.CNOTDihedral.reshape" signature="CNOTDihedral.reshape(input_dims=None, output_dims=None, num_qubits=None)">
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Return a shallow copy with reshaped input and output subsystem dimensions.
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**Parameters**
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* **input\_dims** (*None or tuple*) – new subsystem input dimensions. If None the original input dims will be preserved \[Default: None].
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* **output\_dims** (*None or tuple*) – new subsystem output dimensions. If None the original output dims will be preserved \[Default: None].
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* **num\_qubits** (*None or int*) – reshape to an N-qubit operator \[Default: None].
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**Returns**
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returns self with reshaped input and output dimensions.
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**Return type**
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BaseOperator
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**Raises**
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**QiskitError** – if combined size of all subsystem input dimension or subsystem output dimensions is not constant.
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</Function>
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### tensor
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<Function id="qiskit.ignis.verification.CNOTDihedral.tensor" signature="CNOTDihedral.tensor(other)">
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Return the tensor product operator: self tensor other.
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**Parameters**
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**other** ([*CNOTDihedral*](qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")) – an operator subclass object.
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**Returns**
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the tensor product operator: self tensor other.
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**Return type**
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[CNOTDihedral](qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")
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</Function>
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### to\_circuit
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<Function id="qiskit.ignis.verification.CNOTDihedral.to_circuit" signature="CNOTDihedral.to_circuit()">
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Return a QuantumCircuit implementing the CNOT-Dihedral element.
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**Returns**
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a circuit implementation of the CNOTDihedral object.
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**Return type**
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[QuantumCircuit](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")
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#### Remark:
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Decompose 1 and 2-qubit CNOTDihedral elements.
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**References**
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1. Shelly Garion and Andrew W. Cross, *On the structure of the CNOT-Dihedral group*, [arXiv:2006.12042 \[quant-ph\]](https://arxiv.org/abs/2006.12042)
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2. Andrew W. Cross, Easwar Magesan, Lev S. Bishop, John A. Smolin and Jay M. Gambetta, *Scalable randomised benchmarking of non-Clifford gates*, npj Quantum Inf 2, 16012 (2016).
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</Function>
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### to\_instruction
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<Function id="qiskit.ignis.verification.CNOTDihedral.to_instruction" signature="CNOTDihedral.to_instruction()">
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Return a Gate instruction implementing the CNOTDihedral object.
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</Function>
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### to\_matrix
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<Function id="qiskit.ignis.verification.CNOTDihedral.to_matrix" signature="CNOTDihedral.to_matrix()">
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Convert operator to Numpy matrix.
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</Function>
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### to\_operator
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<Function id="qiskit.ignis.verification.CNOTDihedral.to_operator" signature="CNOTDihedral.to_operator()">
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Convert to an Operator object.
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</Function>
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### transpose
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<Function id="qiskit.ignis.verification.CNOTDihedral.transpose" signature="CNOTDihedral.transpose()">
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Return the transpose of the CNOT-Dihedral element.
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</Function>
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## Attributes
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### dim
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<Attribute id="qiskit.ignis.verification.CNOTDihedral.dim">
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Return tuple (input\_shape, output\_shape).
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</Attribute>
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### key
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<Attribute id="qiskit.ignis.verification.CNOTDihedral.key">
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Return a string representation of a CNOT-dihedral object.
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.ignis.verification.CNOTDihedral.num_qubits">
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Return the number of qubits if a N-qubit operator or None otherwise.
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</Attribute>
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### qargs
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<Attribute id="qiskit.ignis.verification.CNOTDihedral.qargs">
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Return the qargs for the operator.
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</Attribute>
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### settings
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<Attribute id="qiskit.ignis.verification.CNOTDihedral.settings">
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Return operator settings.
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</Attribute>
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</Class>
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