203 lines
6.0 KiB
Plaintext
203 lines
6.0 KiB
Plaintext
---
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title: CCXGate
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description: API reference for qiskit.circuit.library.CCXGate
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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.circuit.library.CCXGate
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---
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# CCXGate
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<Class id="qiskit.circuit.library.CCXGate" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.25/qiskit/circuit/library/standard_gates/x.py" signature="qiskit.circuit.library.CCXGate(label=None, ctrl_state=None)" modifiers="class">
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Bases: [`ControlledGate`](qiskit.circuit.ControlledGate "qiskit.circuit.controlledgate.ControlledGate")
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CCX gate, also known as Toffoli gate.
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Can be applied to a [`QuantumCircuit`](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") with the [`ccx()`](qiskit.circuit.QuantumCircuit#ccx "qiskit.circuit.QuantumCircuit.ccx") and [`toffoli()`](qiskit.circuit.QuantumCircuit#toffoli "qiskit.circuit.QuantumCircuit.toffoli") methods.
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**Circuit symbol:**
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```python
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q_0: ──■──
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│
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q_1: ──■──
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┌─┴─┐
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q_2: ┤ X ├
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└───┘
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```
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**Matrix representation:**
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$$
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\begin{split}CCX q_0, q_1, q_2 =
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I \otimes I \otimes |0 \rangle \langle 0| + CX \otimes |1 \rangle \langle 1| =
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\begin{pmatrix}
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1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\
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0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\
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0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\
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0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\
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0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\
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0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\
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0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\
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0 & 0 & 0 & 1 & 0 & 0 & 0 & 0
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\end{pmatrix}\end{split}
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$$
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<Admonition title="Note" type="note">
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In Qiskit’s convention, higher qubit indices are more significant (little endian convention). In many textbooks, controlled gates are presented with the assumption of more significant qubits as control, which in our case would be q\_2 and q\_1. Thus a textbook matrix for this gate will be:
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```python
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┌───┐
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q_0: ┤ X ├
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└─┬─┘
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q_1: ──■──
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│
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q_2: ──■──
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```
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$$
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\begin{split}CCX\ q_2, q_1, q_0 =
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|0 \rangle \langle 0| \otimes I \otimes I + |1 \rangle \langle 1| \otimes CX =
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\begin{pmatrix}
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1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\
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0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\
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0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\
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0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\
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0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\
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0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\
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0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\
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0 & 0 & 0 & 0 & 0 & 0 & 1 & 0
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\end{pmatrix}\end{split}
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$$
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</Admonition>
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Create new CCX gate.
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## Attributes
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### condition\_bits
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<Attribute id="qiskit.circuit.library.CCXGate.condition_bits">
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Get Clbits in condition.
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</Attribute>
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### ctrl\_state
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<Attribute id="qiskit.circuit.library.CCXGate.ctrl_state">
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Return the control state of the gate as a decimal integer.
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</Attribute>
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### decompositions
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<Attribute id="qiskit.circuit.library.CCXGate.decompositions">
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Get the decompositions of the instruction from the SessionEquivalenceLibrary.
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</Attribute>
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### definition
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<Attribute id="qiskit.circuit.library.CCXGate.definition">
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Return definition in terms of other basic gates. If the gate has open controls, as determined from self.ctrl\_state, the returned definition is conjugated with X without changing the internal \_definition.
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</Attribute>
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### duration
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<Attribute id="qiskit.circuit.library.CCXGate.duration">
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Get the duration.
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</Attribute>
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### label
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<Attribute id="qiskit.circuit.library.CCXGate.label">
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Return instruction label
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</Attribute>
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### name
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<Attribute id="qiskit.circuit.library.CCXGate.name">
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Get name of gate. If the gate has open controls the gate name will become:
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> \<original\_name\_o\<ctrl\_state>
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where \<original\_name> is the gate name for the default case of closed control qubits and \<ctrl\_state> is the integer value of the control state for the gate.
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</Attribute>
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### num\_clbits
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<Attribute id="qiskit.circuit.library.CCXGate.num_clbits">
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Return the number of clbits.
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</Attribute>
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### num\_ctrl\_qubits
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<Attribute id="qiskit.circuit.library.CCXGate.num_ctrl_qubits">
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Get number of control qubits.
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**Returns**
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The number of control qubits for the gate.
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**Return type**
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[int](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)")
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.circuit.library.CCXGate.num_qubits">
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Return the number of qubits.
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</Attribute>
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### params
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<Attribute id="qiskit.circuit.library.CCXGate.params">
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Get parameters from base\_gate.
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**Returns**
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List of gate parameters.
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**Return type**
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[list](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.12)")
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**Raises**
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[**CircuitError**](circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – Controlled gate does not define a base gate
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</Attribute>
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### unit
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<Attribute id="qiskit.circuit.library.CCXGate.unit">
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Get the time unit of duration.
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</Attribute>
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## Methods
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### control
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<Function id="qiskit.circuit.library.CCXGate.control" signature="control(num_ctrl_qubits=1, label=None, ctrl_state=None)">
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Controlled version of this gate.
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**Parameters**
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* **num\_ctrl\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)")) – number of control qubits.
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* **label** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.12)") *or None*) – An optional label for the gate \[Default: None]
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* **ctrl\_state** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)") *or*[*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.12)") *or None*) – control state expressed as integer, string (e.g. ‘110’), or None. If None, use all 1s.
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**Returns**
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controlled version of this gate.
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**Return type**
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[ControlledGate](qiskit.circuit.ControlledGate "qiskit.circuit.ControlledGate")
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</Function>
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### inverse
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<Function id="qiskit.circuit.library.CCXGate.inverse" signature="inverse()">
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Return an inverted CCX gate (also a CCX).
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</Function>
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</Class>
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