Application (`paulie.application`)#

Visualization#

Utilities for visualizing the anti-commutation graph.

`animation.animation_anti_commutation_graph`(...)	Generates an animation showing the transformation of the anti-commutation graph into canonical form.
`plot.plot_anti_commutation_graph`(generators)	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 for finding charges.

Finds the non-commuting charges of a DLA.

Utilities for finding four-point correlation functions.

fourpoint.fourpoint(generators, p, q, r, s)

Computes the four-point correlator of Pauli strings \(P\), \(Q\), \(R\), and \(S\).

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_su_2_n_generators`(...)	Get an optimal 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 \(W\).
`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.

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.

Utilities related to Pauli compilation.

`pauli_compiler.OptimalPauliCompiler`(cfg)	Compiler implementing the construction from arXiv:2408.03294.
`pauli_compiler.PauliCompilerConfig`(k_left, ...)	Configuration of the optimal compiler.
`pauli_compiler.SubsystemCompiler`(cfg)	Compiler for the right subsystem contribution.
`pauli_compiler.SubsystemCompilerConfig`(...)	Configuration of the subsystem compiler.
`pauli_compiler.choose_u_for_b`(k)	Choose the fixed left tag used when coupling to right-side generators.
`pauli_compiler.compile_target`(target, k_left)	Compile a full target Pauli string into a generator sequence.
`pauli_compiler.construct_universal_set`(...)	Construct the universal generator set used by the compiler.
`pauli_compiler.left_a_minimal`(k)	Return the minimal left universal set `{X_i, Z_i}_i \cup {Z^{\otimes k}}`.
`pauli_compiler.left_map_over_a`(v_from, v_to, ...)	Find a left-only adjoint path from `v_from` to `v_to` using BFS.