XXPlusYYGate

XXPlusYYGate(theta, beta=0, label='{XX+YY}')

Bases: qiskit.circuit.gate.Gate

XX+YY interaction gate.

A 2-qubit parameterized XX+YY interaction, also known as an XY gate. Its action is to induce a coherent rotation by some angle between $|01\rangle$ and $|10\rangle$ .

Circuit Symbol:

     ┌───────────────┐
q_0: ┤0              ├
     │  {XX+YY}(θ,β) │
q_1: ┤1              ├
     └───────────────┘

Matrix Representation:

\providecommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{XX+YY}(\theta, \beta)\ q_0, q_1 = RZ_0(-\beta) \cdot \exp\left(-i \frac{\theta}{2} \frac{XX+YY}{2}\right) \cdot RZ_0(\beta) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos\left(\th\right) & -i\sin\left(\th\right)e^{-i\beta} & 0 \\ 0 & -i\sin\left(\th\right)e^{i\beta} & \cos\left(\th\right) & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}\end{split}

Note

In Qiskit’s convention, higher qubit indices are more significant (little endian convention). In the above example we apply the gate on (q_0, q_1) which results in adding the (optional) phase defined by $beta$ on q_0. Instead, if we apply it on (q_1, q_0), the phase is added on q_1. If $beta$ is set to its default value of $0$ , the gate is equivalent in big and little endian.

     ┌───────────────┐
q_0: ┤1              ├
     │  {XX+YY}(θ,β) │
q_1: ┤0              ├
     └───────────────┘

\providecommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{XX+YY}(\theta, \beta)\ q_0, q_1 = RZ_1(-\beta) \cdot \exp\left(-i \frac{\theta}{2} \frac{XX+YY}{2}\right) \cdot RZ_1(\beta) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos\left(\th\right) & -i\sin\left(\th\right)e^{i\beta} & 0 \\ 0 & -i\sin\left(\th\right)e^{-i\beta} & \cos\left(\th\right) & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}\end{split}

Create new XX+YY gate.

Parameters

theta (Union[ParameterExpression, float]) – The rotation angle.
beta (Union[ParameterExpression, float]) – The phase angle.
label (Optional[str]) – The label of the gate.

Methods Defined Here

inverse

XXPlusYYGate.inverse()

Return inverse XX+YY gate (i.e. with the negative rotation angle and same phase angle).

power

XXPlusYYGate.power(exponent)

Raise gate to a power.

Attributes

condition_bits

Get Clbits in condition.

Return type

List[Clbit]

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

Return type

str

name

Return the name.

num_clbits

Return the number of clbits.

num_qubits

Return the number of qubits.

params

return instruction params.

unit

Get the time unit of duration.

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