qml.labs.dla.BDI¶

BDI(op, p=None, q=None, wire=None)[source]¶

Canonical Cartan decomposition of type BDI, given by $\theta: x \mapsto I_{p,q} x I_{p,q}$ .

The matrix $I_{p,q}$ is given by

$I_{p,q}=\text{diag}(\underset{p \text{times}}{\underbrace{1, \dots 1}}, \underset{q \text{times}}{\underbrace{-1, \dots -1}}).$

For $p=q=2^N$ for some integer $N$ , we have $I_{p,q}=Z_0$ .

Note

Note that we work with Hermitian operators internally, so that the input will be multiplied by $i$ before evaluating the involution.

Parameters

op (Union[np.ndarray, PauliSentence, Operator]) – Operator on which the involution is evaluated and for which the parity under the involution is returned.
p (int) – Dimension of first subspace.
q (int) – Dimension of second subspace.
wire (int) – The wire on which the Pauli- $Z$ operator acts to implement the involution. Will default to 0 if None.

Returns

Whether or not the input operator (times $i$ ) is in the eigenspace of the involution $\theta$ with eigenvalue $+1$ .

Return type

bool