# PolyXP¶

Module: pennylane

class PolyXP(q, wires)[source]

An arbitrary second-order polynomial observable.

Represents an arbitrary observable $$P(\x,\p)$$ that is a second order polynomial in the basis $$\mathbf{r} = (\I, \x_0, \p_0, \x_1, \p_1, \ldots)$$.

For first-order observables the representation is a real vector $$\mathbf{d}$$ such that $$P(\x,\p) = \mathbf{d}^T \mathbf{r}$$.

For second-order observables the representation is a real symmetric matrix $$A$$ such that $$P(\x,\p) = \mathbf{r}^T A \mathbf{r}$$.

Used by QNode._pd_analytic() for evaluating arbitrary order-2 CV expectation values.

Details:

• Number of wires: Any
• Number of parameters: 1
• Observable order: 2nd order in the quadrature operators
• Heisenberg representation: $$A$$
Parameters: q (array[float]) – expansion coefficients