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---
title: CNOTDihedral
description: API reference for qiskit.ignis.verification.CNOTDihedral
in_page_toc_min_heading_level: 1
python_api_type: class
python_api_name: qiskit.ignis.verification.CNOTDihedral
---
<span id="qiskit-ignis-verification-cnotdihedral" />
# qiskit.ignis.verification.CNOTDihedral
<Class id="qiskit.ignis.verification.CNOTDihedral" isDedicatedPage={true} github="https://github.com/qiskit-community/qiskit-ignis/tree/stable/0.5/qiskit/ignis/verification/randomized_benchmarking/dihedral.py" signature="CNOTDihedral(data, validate=True)" modifiers="class">
CNOT-dihedral Object Class. The CNOT-dihedral group on num\_qubits qubits is generated by the gates CNOT, T and X.
**References**
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)
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).
Initialize a CNOTDihedral operator object.
### \_\_init\_\_
<Function id="qiskit.ignis.verification.CNOTDihedral.__init__" signature="__init__(data, validate=True)">
Initialize a CNOTDihedral operator object.
</Function>
## Methods
| | |
| ------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------- |
| [`__init__`](#qiskit.ignis.verification.CNOTDihedral.__init__ "qiskit.ignis.verification.CNOTDihedral.__init__")(data\[, validate]) | Initialize a CNOTDihedral operator object. |
| [`add`](#qiskit.ignis.verification.CNOTDihedral.add "qiskit.ignis.verification.CNOTDihedral.add")(other) | Return the linear operator self + other. |
| [`adjoint`](#qiskit.ignis.verification.CNOTDihedral.adjoint "qiskit.ignis.verification.CNOTDihedral.adjoint")() | Return the conjugate transpose of the CNOTDihedral element |
| [`cnot`](#qiskit.ignis.verification.CNOTDihedral.cnot "qiskit.ignis.verification.CNOTDihedral.cnot")(i, j) | Apply a CNOT gate to this element. |
| [`compose`](#qiskit.ignis.verification.CNOTDihedral.compose "qiskit.ignis.verification.CNOTDihedral.compose")(other\[, qargs, front]) | Return the composed operator. |
| [`conjugate`](#qiskit.ignis.verification.CNOTDihedral.conjugate "qiskit.ignis.verification.CNOTDihedral.conjugate")() | Return the conjugate of the CNOTDihedral element. |
| [`copy`](#qiskit.ignis.verification.CNOTDihedral.copy "qiskit.ignis.verification.CNOTDihedral.copy")() | Make a deep copy of current operator. |
| [`dot`](#qiskit.ignis.verification.CNOTDihedral.dot "qiskit.ignis.verification.CNOTDihedral.dot")(other\[, qargs]) | Return the right multiplied operator self \* other. |
| [`expand`](#qiskit.ignis.verification.CNOTDihedral.expand "qiskit.ignis.verification.CNOTDihedral.expand")(other) | Return the tensor product operator: other tensor self. |
| [`flip`](#qiskit.ignis.verification.CNOTDihedral.flip "qiskit.ignis.verification.CNOTDihedral.flip")(i) | Apply X to this element. |
| [`from_circuit`](#qiskit.ignis.verification.CNOTDihedral.from_circuit "qiskit.ignis.verification.CNOTDihedral.from_circuit")(circuit) | Initialize from a QuantumCircuit or Instruction. |
| [`input_dims`](#qiskit.ignis.verification.CNOTDihedral.input_dims "qiskit.ignis.verification.CNOTDihedral.input_dims")(\[qargs]) | Return tuple of input dimension for specified subsystems. |
| [`is_cnotdihedral`](#qiskit.ignis.verification.CNOTDihedral.is_cnotdihedral "qiskit.ignis.verification.CNOTDihedral.is_cnotdihedral")() | Return True if input is a CNOTDihedral element. |
| [`multiply`](#qiskit.ignis.verification.CNOTDihedral.multiply "qiskit.ignis.verification.CNOTDihedral.multiply")(other) | Return the linear operator other \* self. |
| [`output_dims`](#qiskit.ignis.verification.CNOTDihedral.output_dims "qiskit.ignis.verification.CNOTDihedral.output_dims")(\[qargs]) | Return tuple of output dimension for specified subsystems. |
| [`phase`](#qiskit.ignis.verification.CNOTDihedral.phase "qiskit.ignis.verification.CNOTDihedral.phase")(k, i) | Apply an k-th power of T to this element. |
| [`power`](#qiskit.ignis.verification.CNOTDihedral.power "qiskit.ignis.verification.CNOTDihedral.power")(n) | Return the compose of a operator with itself n times. |
| [`reshape`](#qiskit.ignis.verification.CNOTDihedral.reshape "qiskit.ignis.verification.CNOTDihedral.reshape")(\[input\_dims, output\_dims]) | Return a shallow copy with reshaped input and output subsystem dimensions. |
| [`set_atol`](#qiskit.ignis.verification.CNOTDihedral.set_atol "qiskit.ignis.verification.CNOTDihedral.set_atol")(value) | Set the class default absolute tolerance parameter for float comparisons. |
| [`set_rtol`](#qiskit.ignis.verification.CNOTDihedral.set_rtol "qiskit.ignis.verification.CNOTDihedral.set_rtol")(value) | Set the class default relative tolerance parameter for float comparisons. |
| [`subtract`](#qiskit.ignis.verification.CNOTDihedral.subtract "qiskit.ignis.verification.CNOTDihedral.subtract")(other) | Return the linear operator self - other. |
| [`tensor`](#qiskit.ignis.verification.CNOTDihedral.tensor "qiskit.ignis.verification.CNOTDihedral.tensor")(other) | Return the tensor product operator: self tensor other. |
| [`to_circuit`](#qiskit.ignis.verification.CNOTDihedral.to_circuit "qiskit.ignis.verification.CNOTDihedral.to_circuit")() | Return a QuantumCircuit implementing the CNOT-Dihedral element. |
| [`to_instruction`](#qiskit.ignis.verification.CNOTDihedral.to_instruction "qiskit.ignis.verification.CNOTDihedral.to_instruction")() | Return a Gate instruction implementing the CNOTDihedral object. |
| [`to_matrix`](#qiskit.ignis.verification.CNOTDihedral.to_matrix "qiskit.ignis.verification.CNOTDihedral.to_matrix")() | Convert operator to Numpy matrix. |
| [`to_operator`](#qiskit.ignis.verification.CNOTDihedral.to_operator "qiskit.ignis.verification.CNOTDihedral.to_operator")() | Convert to an Operator object. |
| [`transpose`](#qiskit.ignis.verification.CNOTDihedral.transpose "qiskit.ignis.verification.CNOTDihedral.transpose")() | Return the transpose of the CNOT-Dihedral element. |
## Attributes
| | |
| ---------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------- |
| [`atol`](#qiskit.ignis.verification.CNOTDihedral.atol "qiskit.ignis.verification.CNOTDihedral.atol") | The default absolute tolerance parameter for float comparisons. |
| [`dim`](#qiskit.ignis.verification.CNOTDihedral.dim "qiskit.ignis.verification.CNOTDihedral.dim") | Return tuple (input\_shape, output\_shape). |
| [`key`](#qiskit.ignis.verification.CNOTDihedral.key "qiskit.ignis.verification.CNOTDihedral.key") | Return a string representation of a CNOT-dihedral object. |
| [`num_qubits`](#qiskit.ignis.verification.CNOTDihedral.num_qubits "qiskit.ignis.verification.CNOTDihedral.num_qubits") | Return the number of qubits if a N-qubit operator or None otherwise. |
| [`qargs`](#qiskit.ignis.verification.CNOTDihedral.qargs "qiskit.ignis.verification.CNOTDihedral.qargs") | Return the qargs for the operator. |
| [`rtol`](#qiskit.ignis.verification.CNOTDihedral.rtol "qiskit.ignis.verification.CNOTDihedral.rtol") | The relative tolerance parameter for float comparisons. |
### add
<Function id="qiskit.ignis.verification.CNOTDihedral.add" signature="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
</Function>
### adjoint
<Function id="qiskit.ignis.verification.CNOTDihedral.adjoint" signature="adjoint()">
Return the conjugate transpose of the CNOTDihedral element
</Function>
### atol
<Attribute id="qiskit.ignis.verification.CNOTDihedral.atol">
The default absolute tolerance parameter for float comparisons.
</Attribute>
### cnot
<Function id="qiskit.ignis.verification.CNOTDihedral.cnot" signature="cnot(i, j)">
Apply a CNOT gate to this element. Left multiply the element by CNOT\_\{i,j}.
</Function>
### compose
<Function id="qiskit.ignis.verification.CNOTDihedral.compose" signature="compose(other, qargs=None, front=False)">
Return the composed operator.
**Parameters**
* **other** ([*CNOTDihedral*](#qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")) – an operator object.
* **qargs** (*None*) – using specific qargs is not implemented for this operator.
* **front** (*bool*) – if True compose using right operator multiplication, instead of left multiplication \[default: False].
**Returns**
The operator self @ other.
**Return type**
[CNOTDihedral](#qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")
**Raises**
* **QiskitError** – if operators have incompatible dimensions for composition.
* **NotImplementedError** – if qargs is not None.
**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()`](#qiskit.ignis.verification.CNOTDihedral.dot "qiskit.ignis.verification.CNOTDihedral.dot") method.
</Function>
### conjugate
<Function id="qiskit.ignis.verification.CNOTDihedral.conjugate" signature="conjugate()">
Return the conjugate of the CNOTDihedral element.
</Function>
### copy
<Function id="qiskit.ignis.verification.CNOTDihedral.copy" signature="copy()">
Make a deep copy of current operator.
</Function>
### dim
<Attribute id="qiskit.ignis.verification.CNOTDihedral.dim">
Return tuple (input\_shape, output\_shape).
</Attribute>
### dot
<Function id="qiskit.ignis.verification.CNOTDihedral.dot" signature="dot(other, qargs=None)">
Return the right multiplied operator self \* other.
**Parameters**
* **other** ([*CNOTDihedral*](#qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")) – an operator object.
* **qargs** (*None*) – using specific qargs is not implemented for this operator.
**Returns**
The operator self \* other.
**Return type**
[CNOTDihedral](#qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")
**Raises**
* **QiskitError** – if operators have incompatible dimensions for composition.
* **NotImplementedError** – if qargs is not None.
</Function>
### expand
<Function id="qiskit.ignis.verification.CNOTDihedral.expand" signature="expand(other)">
Return the tensor product operator: other tensor self.
**Parameters**
**other** ([*CNOTDihedral*](#qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")) – an operator subclass object.
**Returns**
the tensor product operator: other tensor other.
**Return type**
[CNOTDihedral](#qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")
</Function>
### flip
<Function id="qiskit.ignis.verification.CNOTDihedral.flip" signature="flip(i)">
Apply X to this element. Left multiply the element by X\_i.
</Function>
### from\_circuit
<Function id="qiskit.ignis.verification.CNOTDihedral.from_circuit" signature="from_circuit(circuit)">
Initialize from a QuantumCircuit or Instruction.
**Parameters**
**circuit** ([*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") *or*[*Instruction*](qiskit.circuit.Instruction "qiskit.circuit.Instruction")) – instruction to initialize.
**Returns**
the CNOTDihedral object for the circuit.
**Return type**
[CNOTDihedral](#qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")
**Raises**
**QiskitError** – if the input instruction is not CNOTDihedral or contains classical register instruction.
</Function>
### input\_dims
<Function id="qiskit.ignis.verification.CNOTDihedral.input_dims" signature="input_dims(qargs=None)">
Return tuple of input dimension for specified subsystems.
</Function>
### is\_cnotdihedral
<Function id="qiskit.ignis.verification.CNOTDihedral.is_cnotdihedral" signature="is_cnotdihedral()">
Return True if input is a CNOTDihedral element.
</Function>
### key
<Attribute id="qiskit.ignis.verification.CNOTDihedral.key">
Return a string representation of a CNOT-dihedral object.
</Attribute>
### multiply
<Function id="qiskit.ignis.verification.CNOTDihedral.multiply" signature="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.
</Function>
### num\_qubits
<Attribute id="qiskit.ignis.verification.CNOTDihedral.num_qubits">
Return the number of qubits if a N-qubit operator or None otherwise.
</Attribute>
### output\_dims
<Function id="qiskit.ignis.verification.CNOTDihedral.output_dims" signature="output_dims(qargs=None)">
Return tuple of output dimension for specified subsystems.
</Function>
### phase
<Function id="qiskit.ignis.verification.CNOTDihedral.phase" signature="phase(k, i)">
Apply an k-th power of T to this element. Left multiply the element by T\_i^k.
</Function>
### power
<Function id="qiskit.ignis.verification.CNOTDihedral.power" signature="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.
</Function>
### qargs
<Attribute id="qiskit.ignis.verification.CNOTDihedral.qargs">
Return the qargs for the operator.
</Attribute>
### reshape
<Function id="qiskit.ignis.verification.CNOTDihedral.reshape" signature="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.
</Function>
### rtol
<Attribute id="qiskit.ignis.verification.CNOTDihedral.rtol">
The relative tolerance parameter for float comparisons.
</Attribute>
### set\_atol
<Function id="qiskit.ignis.verification.CNOTDihedral.set_atol" signature="set_atol(value)" modifiers="classmethod">
Set the class default absolute tolerance parameter for float comparisons.
DEPRECATED: use operator.atol = value instead
</Function>
### set\_rtol
<Function id="qiskit.ignis.verification.CNOTDihedral.set_rtol" signature="set_rtol(value)" modifiers="classmethod">
Set the class default relative tolerance parameter for float comparisons.
DEPRECATED: use operator.rtol = value instead
</Function>
### subtract
<Function id="qiskit.ignis.verification.CNOTDihedral.subtract" signature="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
</Function>
### tensor
<Function id="qiskit.ignis.verification.CNOTDihedral.tensor" signature="tensor(other)">
Return the tensor product operator: self tensor other.
**Parameters**
**other** ([*CNOTDihedral*](#qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")) – an operator subclass object.
**Returns**
the tensor product operator: self tensor other.
**Return type**
[CNOTDihedral](#qiskit.ignis.verification.CNOTDihedral "qiskit.ignis.verification.CNOTDihedral")
</Function>
### to\_circuit
<Function id="qiskit.ignis.verification.CNOTDihedral.to_circuit" signature="to_circuit()">
Return a QuantumCircuit implementing the CNOT-Dihedral element.
**Returns**
a circuit implementation of the CNOTDihedral object.
**Return type**
[QuantumCircuit](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")
**Remark:**
Decompose 1 and 2-qubit CNOTDihedral elements.
**References**
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)
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).
</Function>
### to\_instruction
<Function id="qiskit.ignis.verification.CNOTDihedral.to_instruction" signature="to_instruction()">
Return a Gate instruction implementing the CNOTDihedral object.
</Function>
### to\_matrix
<Function id="qiskit.ignis.verification.CNOTDihedral.to_matrix" signature="to_matrix()">
Convert operator to Numpy matrix.
</Function>
### to\_operator
<Function id="qiskit.ignis.verification.CNOTDihedral.to_operator" signature="to_operator()">
Convert to an Operator object.
</Function>
### transpose
<Function id="qiskit.ignis.verification.CNOTDihedral.transpose" signature="transpose()">
Return the transpose of the CNOT-Dihedral element.
</Function>
</Class>
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