# qiskit.circuit.library.CU3Gate¶

class CU3Gate(theta, phi, lam, label=None, ctrl_state=None)[source]

Controlled-U3 gate (3-parameter two-qubit gate).

This is a controlled version of the U3 gate (generic single qubit rotation). It is restricted to 3 parameters, and so cannot cover generic two-qubit controlled gates).

Circuit symbol:

q_0: ──────■──────
┌─────┴─────┐
q_1: ┤ U3(ϴ,φ,λ) ├
└───────────┘


Matrix representation:

\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}CU3(\theta, \phi, \lambda)\ q_0, q_1 = I \otimes |0\rangle\langle 0| + U3(\theta,\phi,\lambda) \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos(\th) & 0 & -e^{i\lambda}\sin(\th) \\ 0 & 0 & 1 & 0 \\ 0 & e^{i\phi}\sin(\th) & 0 & e^{i(\phi+\lambda)}\cos(\th) \end{pmatrix}\end{split}\end{aligned}\end{align}

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: ┤ U3(ϴ,φ,λ) ├
└─────┬─────┘
q_1: ──────■──────

$\begin{split}CU3(\theta, \phi, \lambda)\ q_1, q_0 = |0\rangle\langle 0| \otimes I + |1\rangle\langle 1| \otimes U3(\theta,\phi,\lambda) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos(\th) & -e^{i\lambda}\sin(\th) \\ 0 & 0 & e^{i\phi}\sin(\th) & e^{i(\phi+\lambda)}\cos(\th) \end{pmatrix}\end{split}$

Create new CU3 gate.

__init__(theta, phi, lam, label=None, ctrl_state=None)[source]

Create new CU3 gate.

Methods

 __init__(theta, phi, lam[, label, ctrl_state]) Create new CU3 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 classical and value val. control([num_ctrl_qubits, label, ctrl_state]) Return controlled version of gate. copy([name]) Copy of the instruction. Return inverted CU3 gate. 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 gate 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

Type renvoyé

Instruction

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]], []


The general broadcasting rules are:

• 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], ...]

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

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

Type renvoyé

Tuple[List, List]

Renvoie

A tuple with single arguments.

Lève

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 classical and value val.

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

Return controlled version of gate. See ControlledGate for usage.

Paramètres
• num_ctrl_qubits (Optional[int]) – number of controls to add to gate (default=1)

• label (Optional[str]) – optional gate label

• ctrl_state (Union[int, str, None]) – The control state in decimal or as a bitstring (e.g. “111”). If None, use 2**num_ctrl_qubits-1.

Renvoie

Controlled version of gate. This default algorithm uses num_ctrl_qubits-1 ancillae qubits so returns a gate of size num_qubits + 2*num_ctrl_qubits - 1.

Type renvoyé

qiskit.circuit.ControlledGate

Lève

QiskitError – unrecognized mode or invalid ctrl_state

copy(name=None)

Copy of the instruction.

Paramètres

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

Renvoie

a copy of the current instruction, with the name

updated if it was provided

Type renvoyé

qiskit.circuit.Instruction

property ctrl_state

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

Type renvoyé

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.

Type renvoyé

List

property duration

Get the duration.

inverse()[source]

Return inverted CU3 gate.

$$CU3(\theta,\phi,\lambda)^{\dagger} =CU3(-\theta,-\phi,-\lambda)$$)

is_parameterized()

Return True .IFF. instruction is parameterized else False

property label

Return gate label

Type renvoyé

str

mirror()

DEPRECATED: use instruction.reverse_ops().

Renvoie

a new instruction with sub-instructions

reversed.

Type renvoyé

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.

Type renvoyé

str

property num_ctrl_qubits

Get number of control qubits.

Renvoie

The number of control qubits for the gate.

Type renvoyé

int

property params

Get parameters from base_gate.

Renvoie

List of gate parameters.

Type renvoyé

list

Lève

CircuitError – Controlled gate does not define a base gate

power(exponent)

Creates a unitary gate as gate^exponent.

Paramètres

exponent (float) – Gate^exponent

Renvoie

To which to_matrix is self.to_matrix^exponent.

Type renvoyé

qiskit.extensions.UnitaryGate

Lève

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.

Paramètres

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

Renvoie

Containing the definition.

Type renvoyé

qiskit.circuit.Instruction

Lève

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.

Renvoie

a new instruction with

sub-instructions reversed.

Type renvoyé

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.

Paramètres

other (instruction) – other instruction.

Renvoie

are self and other equal up to parameter expressions.

Type renvoyé

bool

to_matrix()

Return a Numpy.array for the gate unitary matrix.

Renvoie

if the Gate subclass has a matrix definition.

Type renvoyé

np.ndarray

Lève

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