Application (`paulie.application`)#

Visualization#

Utilities for visualizing the anti-commutation graph.

Plot a canonical anti-commutation graph of a set of generators.

Utilities related to average Pauli weights.

`average_pauli_weight.average_pauli_weight`(o)	Calculates the average Pauli weight (influence) for an operator \(O\).
`average_pauli_weight.get_pauli_weights`(...)	Generates the weight \(\|P\|\) for each of the \(4^{\text{number qubits}}\) Pauli operators.
`average_pauli_weight.quantum_fourier_entropy`(o)	Finds the quantum Fourier entropy of an operator \(O\).

Utilities related to \(\mathfrak{su}(2^n)\) generators.

`get_optimal_su2_n.get_optimal_edges_su_2_n`(ng)	Get the optimal number of edges in the anticommutation graph for \(\mathfrak{su}(2^{n})\).
`get_optimal_su2_n.get_optimal_universal_generators`(n)	Get an optimal universal generator set for \(\mathfrak{su}(2^{n})\).

Utilities related to different DLA properties.

`average_graph_complexity.average_graph_complexity`(...)	Get the average graph complexity of a Pauli string with respect to the time evolution generated by a given generator set.
`otoc.average_otoc`(generators, v, w)	Finds the Haar averaged out-of-time-order correlator \(F\) between two Pauli strings \(V\) and \(W\).
`otoc.fourpoint`(generators, m, q, r, s)	Computes the four-point correlator of Pauli strings \(P\), \(Q\), \(R\), and \(S\).
`second_moment.second_moment`(operator_m, ...)	Computes the second-order twirl of an operator \(M\) by projecting it onto the subspace of quadratic symmetries of a DLA.

Expectations over uniform Pauli pairs for a given unitary (contrast with Haar-averaged average_otoc() over a DLA).

`otoc.otoc_fixed_unitary`(u, p1, p2, *[, ...])	Out-of-time-order correlator for a fixed unitary \(U\) and Pauli strings \(P_1\), \(P_2\):
`otoc.mean_abs_otoc_uniform`(u, *[, method, ...])	Uniform expectation of \(\lvert\mathrm{OTOC}(U,P_1,P_2)\rvert\) over independent \(P_1,P_2 \in \{I,X,Y,Z\}^{\otimes n}\) (each uniform on \(4^n\) strings).
`otoc.pauli_instability`(u, *[, method, ...])	Pauli instability (Definition 1):

Utilities related to matrix decompositions.

`matrix_decomposition.matrix_decomposition`(matrix)	Returns the weight vector corresponding to the Pauli basis decomposition of a matrix.
`matrix_decomposition.matrix_decomposition_diagonal`(diag)	Returns the weight vector corresponding to the Pauli basis decomposition of a diagonal matrix.