paulie.application.otoc.average_otoc#
- paulie.application.otoc.average_otoc(generators, v, w)#
Finds the Haar averaged out-of-time-order correlator \(F\) between two Pauli strings \(V\) and \(W\).
We write it as
\[\mathbb{E}_U[F(W, U^\dagger V U)] = \frac{\mathbb{E}_U[\mathrm{tr} (W U^\dagger V U W U^\dagger V U)]}{d}\]where \(U\) is sampled according to the Haar measure on the Lie group corresponding to the DLA generated by generators and \(d\) is the dimension of the Hilbert space.
We can compute this via the commutator graph as
\[F=1 - 2\frac{|\{W, P\} = 0 : P\text{ in connected component of }V|} {|\text{connected component of }V|}\](arXiV:2502.16404)
- Parameters:
generators (PauliStringCollection) – Generating set of the Pauli string DLA.
v (PauliString) – Pauli string \(V\)
w (PauliString) – Pauli string \(W\)
- Returns:
Haar averaged out-of-time-order correlator \(F\) between two Pauli strings \(V\) and \(W\).
- Return type: