qiskit.circuit.library.CU3Gate¶

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

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:

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

Bemerkung

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)[Quellcode]¶: 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 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 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

Rückgabetyp: 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], ...]

Parameter

qargs (List) – List of quantum bit arguments.
cargs (List) – List of classical bit arguments.

Rückgabetyp

Tuple[List, List]

Rückgabe

A tuple with single arguments.

Verursacht

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.

Parameter

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.

Rückgabe

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.

Rückgabetyp

qiskit.circuit.ControlledGate

Verursacht

QiskitError – unrecognized mode or invalid ctrl_state

copy(name=None)¶

Copy of the instruction.

Parameter

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

Rückgabe

a copy of the current instruction, with the name: updated if it was provided

Rückgabetyp

qiskit.circuit.Instruction

property ctrl_state¶

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

Rückgabetyp: 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.

Rückgabetyp: List

property duration¶: Get the duration.

inverse()[Quellcode]¶

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

Rückgabetyp: str

mirror()¶

DEPRECATED: use instruction.reverse_ops().

Rückgabe

a new instruction with sub-instructions: reversed.

Rückgabetyp

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.

Rückgabetyp: str

property num_ctrl_qubits¶

Get number of control qubits.

Rückgabe: The number of control qubits for the gate.
Rückgabetyp: int

property params¶

Get parameters from base_gate.

Rückgabe: List of gate parameters.
Rückgabetyp: list
Verursacht: CircuitError – Controlled gate does not define a base gate

power(exponent)¶

Creates a unitary gate as gate^exponent.

Parameter: exponent (float) – Gate^exponent
Rückgabe: To which to_matrix is self.to_matrix^exponent.
Rückgabetyp: qiskit.extensions.UnitaryGate
Verursacht: 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.

Parameter: n (int) – Number of times to repeat the instruction
Rückgabe: Containing the definition.
Rückgabetyp: qiskit.circuit.Instruction
Verursacht: 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.

Rückgabe

a new instruction with: sub-instructions reversed.

Rückgabetyp

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.

Parameter: other (instruction) – other instruction.
Rückgabe: are self and other equal up to parameter expressions.
Rückgabetyp: bool

to_matrix()¶

Return a Numpy.array for the gate unitary matrix.

Rückgabe: if the Gate subclass has a matrix definition.
Rückgabetyp: np.ndarray
Verursacht: 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