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.

Attributes

ctrl_state

Type: int

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

Type: List

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

label

Type: str

Return gate label

Return type

str

params

return instruction params.

Methods

add_decomposition

CU3Gate.add_decomposition(decomposition)

Add a decomposition of the instruction to the SessionEquivalenceLibrary.

assemble

CU3Gate.assemble()

Assemble a QasmQobjInstruction

Return type

Instruction

broadcast_arguments

CU3Gate.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

CU3Gate.c_if(classical, val)

Add classical condition on register classical and value val.

control

CU3Gate.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

CU3Gate.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

inverse

CU3Gate.inverse()

Return inverted CU3 gate.

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

is_parameterized

CU3Gate.is_parameterized()

Return True .IFF. instruction is parameterized else False

mirror

CU3Gate.mirror()

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

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

Returns

a fresh gate with sub-gates reversed

Return type

qiskit.circuit.Instruction

power

CU3Gate.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

CU3Gate.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

CU3Gate.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.

to_matrix

CU3Gate.to_matrix()

Return a Numpy.array for the gate unitary matrix.

Raises

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

Return type

ndarray

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