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CXGate

class qiskit.circuit.library.CXGate(label=None, ctrl_state=None)

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Bases: ControlledGate

Controlled-X gate.

Can be applied to a QuantumCircuit with the cx() and cnot() methods.

Circuit symbol:

q_0: ──■──
     ┌─┴─┐
q_1: ┤ X ├
     └───┘

Matrix representation:

CX q0,q1=I⊗∣0⟩⟨0∣+X⊗∣1⟩⟨1∣=(1000000100100100)\begin{split}CX\ q_0, q_1 = I \otimes |0\rangle\langle0| + X \otimes |1\rangle\langle1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{pmatrix}\end{split}
Note

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_1. Thus a textbook matrix for this gate will be:

     ┌───┐
q_0: ┤ X ├
     └─┬─┘
q_1: ──■──
CX q1,q0=∣0⟩⟨0∣⊗I+∣1⟩⟨1∣⊗X=(1000010000010010)\begin{split}CX\ q_1, q_0 = |0 \rangle\langle 0| \otimes I + |1 \rangle\langle 1| \otimes X = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{pmatrix}\end{split}

In the computational basis, this gate flips the target qubit if the control qubit is in the ∣1⟩|1\rangle state. In this sense it is similar to a classical XOR gate.

‘∣a,b⟩→∣a,a⊕b⟩‘`|a, b\rangle \rightarrow |a, a \oplus b\rangle`

Create new CX gate.

Attributes

condition_bits

Get Clbits in condition.

ctrl_state

Return the control state of the gate as a decimal integer.

decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

definition

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.

duration

Get the duration.

label

Return instruction label

name

Get name of gate. If the gate has open controls the gate name will become:

<original_name_o<ctrl_state>

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.

num_clbits

Return the number of clbits.

num_ctrl_qubits

Get number of control qubits.

Returns

The number of control qubits for the gate.

Return type

int

num_qubits

Return the number of qubits.

params

Get parameters from base_gate.

Returns

List of gate parameters.

Return type

list

Raises

CircuitError – Controlled gate does not define a base gate

unit

Get the time unit of duration.

Methods

control

control(num_ctrl_qubits=1, label=None, ctrl_state=None)

Return a controlled-X gate with more control lines.

Parameters

  • num_ctrl_qubits (int) – number of control qubits.
  • label (str or None) – An optional label for the gate [Default: None]
  • ctrl_state (int orstr or None) – control state expressed as integer, string (e.g. ‘110’), or None. If None, use all 1s.

Returns

controlled version of this gate.

Return type

ControlledGate

inverse

inverse()

Return inverted CX gate (itself).

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