qiskit.circuit.library.CUGate

class CUGate(theta, phi, lam, gamma, label=None, ctrl_state=None)

Controlled-U gate (4-parameter two-qubit gate).

This is a controlled version of the U gate (generic single qubit rotation), including a possible global phase \(e^{i\gamma}\) of the U gate.

Circuit symbol:

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

Matrix representation:

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

注釈

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

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

Create new CU gate.

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

Create new CU gate.

Methods

__init__(theta, phi, lam, gamma[, label, …])	Create new CU 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 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 CU 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.
to_matrix()	Return a numpy.array for the CU gate.
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
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

戻り値の型

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], ...]
  

パラメータ

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

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

戻り値の型

Tuple[List, List]

戻り値

A tuple with single arguments.

例外

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.

パラメータ

• 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.

戻り値

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.

戻り値の型

qiskit.circuit.ControlledGate

例外

QiskitError – unrecognized mode or invalid ctrl_state

copy(name=None)

Copy of the instruction.

パラメータ

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

戻り値

a copy of the current instruction, with the name

updated if it was provided

戻り値の型

qiskit.circuit.Instruction

property ctrl_state

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

戻り値の型

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.

戻り値の型

List

property duration

Get the duration.

inverse()

Return inverted CU gate.

\(CU(\theta,\phi,\lambda,\gamma)^{\dagger} = CU(-\theta,-\phi,-\lambda,-\gamma)\))

is_parameterized()

Return True .IFF. instruction is parameterized else False

property label

Return gate label

戻り値の型

str

mirror()

DEPRECATED: use instruction.reverse_ops().

戻り値

a new instruction with sub-instructions

reversed.

戻り値の型

qiskit.circuit.Instruction

property num_ctrl_qubits

Get number of control qubits.

戻り値

The number of control qubits for the gate.

戻り値の型

int

property params

Get parameters from base_gate.

戻り値

List of gate parameters.

戻り値の型

list

例外

CircuitError – Controlled gate does not define a base gate

power(exponent)

Creates a unitary gate as gate^exponent.

パラメータ

exponent (float) – Gate^exponent

戻り値

To which to_matrix is self.to_matrix^exponent.

戻り値の型

qiskit.extensions.UnitaryGate

例外

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.

パラメータ

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

戻り値

Containing the definition.

戻り値の型

qiskit.circuit.Instruction

例外

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.

戻り値

a new instruction with

sub-instructions reversed.

戻り値の型

qiskit.circuit.Instruction

to_matrix()

Return a numpy.array for the CU gate.

property unit

Get the time unit of duration.

validate_parameter(parameter)

Gate parameters should be int, float, or ParameterExpression