# qiskit.circuit.library.CXGate¶

class CXGate(label=None, ctrl_state=None)[source]

Controlled-X gate.

Circuit symbol:

q_0: ──■──
┌─┴─┐
q_1: ┤ X ├
└───┘


Matrix representation:

$\begin{split}CX\ q_0, q_1 = I \otimes |0\rangle\langle0| + X \otimes |1\rangle\langle1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{pmatrix}\end{split}$

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: ──■──

$\begin{split}CX\ q_1, q_0 = |0 \rangle\langle 0| \otimes I + |1 \rangle\langle 1| \otimes X = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{pmatrix}\end{split}$

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

$|a, b\rangle \rightarrow |a, a \oplus b\rangle$

Create new CX gate.

__init__(label=None, ctrl_state=None)[source]

Create new CX gate.

Methods

 __init__([label, ctrl_state]) Create new CX gate. add_decomposition(decomposition) Add a decomposition of the instruction to the SessionEquivalenceLibrary. Assemble a QasmQobjInstruction broadcast_arguments(qargs, cargs) Validation and handling of the arguments and its relationship. c_if(classical, val) Add classical condition on register or cbit classical and value val. control([num_ctrl_qubits, label, ctrl_state]) Return a controlled-X gate with more control lines. copy([name]) Copy of the instruction. Return inverted CX gate (itself). Return True .IFF. DEPRECATED: use instruction.reverse_ops(). power(exponent) Creates a unitary gate as gate^exponent. Return a default OpenQASM string for the instruction. Creates an instruction with gate repeated n amount of times. For a composite instruction, reverse the order of sub-instructions. soft_compare(other) Soft comparison between gates. Return a Numpy.array for the gate unitary matrix. validate_parameter(parameter) Gate parameters should be int, float, or ParameterExpression

Attributes

 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. duration Get the duration. label Return instruction label name Get name of gate. num_ctrl_qubits Get number of control qubits. params Get parameters from base_gate. unit Get the time unit of duration.
add_decomposition(decomposition)

Add a decomposition of the instruction to the SessionEquivalenceLibrary.

assemble()

Assemble a QasmQobjInstruction

broadcast_arguments(qargs, cargs)

Validation and handling of the arguments and its relationship.

For example, cx([q[0],q[1]], q[2]) means cx(q[0], q[2]); cx(q[1], q[2]). This method yields the arguments in the right grouping. In the given example:

in: [[q[0],q[1]], q[2]],[]
outs: [q[0], q[2]], []
[q[1], q[2]], []


• If len(qargs) == 1:

[q[0], q[1]] -> [q[0]],[q[1]]

• If len(qargs) == 2:

[[q[0], q[1]], [r[0], r[1]]] -> [q[0], r[0]], [q[1], r[1]]
[[q[0]], [r[0], r[1]]]       -> [q[0], r[0]], [q[0], r[1]]
[[q[0], q[1]], [r[0]]]       -> [q[0], r[0]], [q[1], r[0]]

• If len(qargs) >= 3:

[q[0], q[1]], [r[0], r[1]],  ...] -> [q[0], r[0], ...], [q[1], r[1], ...]

Parameters
• qargs (List) – List of quantum bit arguments.

• cargs (List) – List of classical bit arguments.

Return type

Tuple[List, List]

Returns

A tuple with single arguments.

Raises

CircuitError – If the input is not valid. For example, the number of arguments does not match the gate expectation.

c_if(classical, val)

Add classical condition on register or cbit classical and value val.

control(num_ctrl_qubits=1, label=None, ctrl_state=None)[source]

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 or str 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

copy(name=None)

Copy of the instruction.

Parameters

name (str) – name to be given to the copied circuit, if None then the name stays the same.

Returns

a copy of the current instruction, with the name

updated if it was provided

Return type

qiskit.circuit.Instruction

property ctrl_state

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

Return type

int

property decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

property 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.

Return type

List

property duration

Get the duration.

inverse()[source]

Return inverted CX gate (itself).

is_parameterized()

Return True .IFF. instruction is parameterized else False

property label

Return instruction label

Return type

str

mirror()

DEPRECATED: use instruction.reverse_ops().

Returns

a new instruction with sub-instructions

reversed.

Return type

qiskit.circuit.Instruction

property 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.

Return type

str

property num_ctrl_qubits

Get number of control qubits.

Returns

The number of control qubits for the gate.

Return type

int

property params

Get parameters from base_gate.

Returns

List of gate parameters.

Return type

list

Raises

CircuitError – Controlled gate does not define a base gate

power(exponent)

Creates a unitary gate as gate^exponent.

Parameters

exponent (float) – Gate^exponent

Returns

To which to_matrix is self.to_matrix^exponent.

Return type

qiskit.extensions.UnitaryGate

Raises

CircuitError – If Gate is not unitary

qasm()

Return a default OpenQASM string for the instruction.

Derived instructions may override this to print in a different format (e.g. measure q[0] -> c[0];).

repeat(n)

Creates an instruction with gate repeated n amount of times.

Parameters

n (int) – Number of times to repeat the instruction

Returns

Containing the definition.

Return type

qiskit.circuit.Instruction

Raises

CircuitError – If n < 1.

reverse_ops()

For a composite instruction, reverse the order of sub-instructions.

This is done by recursively reversing all sub-instructions. It does not invert any gate.

Returns

a new instruction with

sub-instructions reversed.

Return type

qiskit.circuit.Instruction

soft_compare(other)

Soft comparison between gates. Their names, number of qubits, and classical bit numbers must match. The number of parameters must match. Each parameter is compared. If one is a ParameterExpression then it is not taken into account.

Parameters

other (instruction) – other instruction.

Returns

are self and other equal up to parameter expressions.

Return type

bool

to_matrix()

Return a Numpy.array for the gate unitary matrix.

Returns

if the Gate subclass has a matrix definition.

Return type

np.ndarray

Raises

CircuitError – If a Gate subclass does not implement this method an exception will be raised when this base class method is called.

property unit

Get the time unit of duration.

validate_parameter(parameter)

Gate parameters should be int, float, or ParameterExpression