Skip to main contentIBM Quantum Documentation
This page is from an old version of Qiskit SDK Go to the latest version

XXPlusYYGate

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

GitHub

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⟩|01\rangle and ∣10⟩|10\rangle.

Circuit Symbol:

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

Matrix Representation:

RXX+YY(θ,β) q0,q1=RZ0(−β)⋅exp⁡(−iθ2XX+YY2)⋅RZ0(β)=(10000cos⁡(th⁡)−isin⁡(th⁡)e−iβ00−isin⁡(th⁡)eiβcos⁡(th⁡)00001)\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 betabeta on q_0. Instead, if we apply it on (q_1, q_0), the phase is added on q_1. If betabeta is set to its default value of 00, the gate is equivalent in big and little endian.

     ┌───────────────┐
q_0: ┤1              ├
     │  {XX+YY}(θ,β) │
q_1: ┤0              ├
     └───────────────┘
RXX+YY(θ,β) q0,q1=RZ1(−β)⋅exp⁡(−iθ2XX+YY2)⋅RZ1(β)=(10000cos⁡(th⁡)−isin⁡(th⁡)eiβ00−isin⁡(th⁡)e−iβcos⁡(th⁡)00001)\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

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.

Was this page helpful?
Report a bug or request content on GitHub.