qiskit.circuit.library.CU3Gate

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

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:

\providecommand{\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}

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

__init__(theta, phi, lam, label=None, ctrl_state=None)

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`()	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 controlled version of gate.
`copy`([name])	Copy of the instruction.
`inverse`()	Return inverted CU3 gate.
`is_parameterized`()	Return True .IFF.
`mirror`()	DEPRECATED: use instruction.reverse_ops().
`power`(exponent)	Creates a unitary gate as gate^exponent.
`qasm`()	Return a default OpenQASM string for the instruction.
`repeat`(n)	Creates an instruction with gate repeated n amount of times.
`reverse_ops`()	For a composite instruction, reverse the order of sub-instructions.
`soft_compare`(other)	Soft comparison between gates.
`to_matrix`()	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

add_decomposition(decomposition)

Add a decomposition of the instruction to the SessionEquivalenceLibrary.

assemble

assemble()

Assemble a QasmQobjInstruction

broadcast_arguments

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], ...]

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

c_if(classical, val)

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

control

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

Return controlled version of gate. See ControlledGate for usage.

Parameters

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.

Returns

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.

Return type

qiskit.circuit.ControlledGate

Raises

QiskitError – unrecognized mode or invalid ctrl_state

copy

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

ctrl_state

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

Return type

int

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.

Return type

List

duration

Get the duration.

inverse

inverse()

Return inverted CU3 gate.

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

is_parameterized

is_parameterized()

Return True .IFF. instruction is parameterized else False

label

Return instruction label

Return type

str

mirror

mirror()

DEPRECATED: use instruction.reverse_ops().

Returns

a new instruction with sub-instructions

reversed.

Return type

qiskit.circuit.Instruction

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

num_ctrl_qubits

Get number of control qubits.

Returns

The number of control qubits for the gate.

Return type

int

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

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

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

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

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

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

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.

unit

Get the time unit of duration.

validate_parameter

validate_parameter(parameter)

Gate parameters should be int, float, or ParameterExpression

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