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
0ifNone.
- Returns
Whether or not the input operator (times \(i\)) is in the eigenspace of the involution \(\theta\) with eigenvalue \(+1\).
- Return type
bool