CUGate¶
- class CUGate(theta, phi, lam, gamma, label=None, ctrl_state=None)[source]¶
Bases:
qiskit.circuit.controlledgate.ControlledGate
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.
Can be applied to a
QuantumCircuit
with thecu()
method.Circuit symbol:
q_0: ──────■────── ┌─────┴──────┐ q_1: ┤ U(ϴ,φ,λ,γ) ├ └────────────┘
Matrix representation:
\[ \begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}CU(\theta, \phi, \lambda, \gamma)\ q_0, q_1 = I \otimes |0\rangle\langle 0| + e^{i\gamma} U(\theta,\phi,\lambda) \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & e^{i\gamma}\cos(\th) & 0 & -e^{i(\gamma + \lambda)}\sin(\th) \\ 0 & 0 & 1 & 0 \\ 0 & e^{i(\gamma+\phi)}\sin(\th) & 0 & e^{i(\gamma+\phi+\lambda)}\cos(\th) \end{pmatrix}\end{split}\end{aligned}\end{align} \]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: ┤ U(ϴ,φ,λ,γ) ├ └─────┬──────┘ q_1: ──────■───────
\[\begin{split}CU(\theta, \phi, \lambda, \gamma)\ q_1, q_0 = |0\rangle\langle 0| \otimes I + e^{i\gamma}|1\rangle\langle 1| \otimes U(\theta,\phi,\lambda) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & e^{i\gamma} \cos(\th) & -e^{i(\gamma + \lambda)}\sin(\th) \\ 0 & 0 & e^{i(\gamma + \phi)}\sin(\th) & e^{i(\gamma + \phi+\lambda)}\cos(\th) \end{pmatrix}\end{split}\]Create new CU gate.
Methods Defined Here
Return inverted CU gate.
Attributes
- 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.
- label¶
Return instruction label
- Return type
str
- 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_clbits¶
Return the number of clbits.
- num_ctrl_qubits¶
Get number of control qubits.
- Returns
The number of control qubits for the gate.
- Return type
int
- num_qubits¶
Return the number of qubits.
- params¶
Get parameters from base_gate.
- Returns
List of gate parameters.
- Return type
list
- Raises
CircuitError – Controlled gate does not define a base gate
- unit¶
Get the time unit of duration.