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Appendix D — Quick reference of the qang 0.14.0 API

This is the list of every module of the qang package at version 0.14.0, with its public names: those in __all__ or, if the module does not define it, the public functions and classes it declares. tools/make_appendices.py generates it by importing each module, so the list is the code’s own and not a copy. The signature and documentation of each name are in help(qang.<module>.<name>).

Table D.1: The modules of qang 0.14.0.
module what it does names
algebra Closed-form qg algebra: the universal gate, reflections and transition probabilities; Cartan subalgebra (§166). 9
algorithms Textbook algorithms in Qiskit: teleportation, superdense coding, Grover. 9
angular The four quantum numbers of an electron in qg (§155). 17
ansatze Reusable variational ansätze, including qg layers. 4
channels Single-qubit channels as affine maps of the qg vector (§162). 7
circuits Circuit constructors (Bell, GHZ, W, graph, Dicke) and their readings. 14
cirq_gate qg as native Cirq gates. 5
clock_comparison Differential phase between two clocks and the gravitational shift. 5
complementarity Wave–particle duality and entropic uncertainty in qg. 8
core The qang (qg) unit and the Qang class. 2
fisher Fisher information, shift rules and the natural gradient in qg (§159). 14
formulation The 15 gates and 14 algorithms in qg language; the local radius (Appendix A, Chapter 5). 48
geometric Geometric phase (Berry, Pancharatnam) in qg units. 8
gradients The coordinate singularity at the poles and its regularizations. 17
ibm qg readings on IBM Runtime: weight-preservation pass, readout correction, chains, ZNE (§137). 30
integrations qang inside other libraries: one submodule per library (Chapter 35). 12
interop qg readings from any SDK’s results with one qubit order (§130). 10
iqm qg readings on IQM: readout from the poles or the error profile, filter, chain choice (Chapter 31). 7
kernels Quantum kernels with the qg filter (§161). 6
knitting Sampling cost of circuit cutting. 4
mixed The qang unit for mixed states and POVMs. 11
multiqubit The qang unit for multi-qubit registers: marginals, entropies, correlations. 14
neutrino Neutrino flavour oscillations in qg (§151; Chapters 9–11). 38
pennylane_gate qg as native, differentiable PennyLane operations; filtered readout. 6
phase The deferred qg_Φ phase unit. 2
polarization Polarized light in qg units: Stokes, Jones, Mueller (§83; Chapter 6). 17
postselection Teleportation with postselection: closed timelike curves and black-hole decoding (Chapters 14–15). 8
probability The qang probability equation and the milli-qang (§167; Chapter 1). 13
proportions The qang angle as the arcsine transformation of a proportion. 9
pulse_area Pulse area of fractional gates: the minimal-area rule (§160). 6
qec The 3-qubit bit-flip code with syndromes read in qg. 6
qga The angular qga scale: 1000 qga per turn; conversions to radians, \(p_0\) and m-qg, Fisher and Berry phase in qga (Chapter 1). 15
qiskit_gate qg as a native Qiskit gate. 5
qiskit_ml The weight QNN inside qiskit-machine-learning (§140). 4
qml Weight-conserving quantum neural networks, with and without the filter (§75–§80; Chapter 20). 4
qpon Teleportation through a passive optical network, discrete variables (§157; Chapters 12–13). 17
qsp Quantum signal processing in qg (§134). 8
sectors Conserved-sector tools for the qg filter and the echo (§20, §60, §66, §68; Appendix C). 9
statistics Error propagation between probability and angle, estimators and intervals. 25
transformations Closed-form transformations between qang-parameterized states. 1
varqte Variational real-time evolution (McLachlan) with a weight-preserving ansatz (§162). 6

D.1 Public names by module

  • algebra: u3_qang, transition_matrix, householder_qg, grover_diffuser_qg, qg_vector, transition_probability, cartan_generators, cartan_values, populations_from_cartan
  • algorithms: teleportation_circuit, teleportation_output_fidelity, superdense_coding_circuit, decode_superdense_coding, grover_oracle, grover_diffusion, grover_optimal_iterations, grover_circuit, grover_success_probability
  • angular: m_from_weight, weight_from_m, m_distribution, qg_z_spin, qg_s_spin, coherent_m_distribution, qang_angle_of_eigenstate, vector_model_angle, transverse_spread, dicke_state, p_orbital, spin_operators, shell_quantum_numbers, shell_register_qubits, shell_l_spectrum, j_squared_from_swaps, l_from_j_squared
  • ansatze: single_excitation_ansatz, hardware_efficient_ansatz, qg_ry_layer, hardware_efficient_ansatz_qg
  • channels: apply_kraus, bloch_affine, qg_after, amplitude_damping, phase_damping, depolarizing, thermal_relaxation
  • circuits: qg_z_profile_of_circuit, joint_qg_s_of_circuit, bell_circuit, ghz_circuit, w_circuit, graph_state_circuit, linear_cluster_state_circuit, dicke_state_circuit, ghz_qg_z_profile, ghz_joint_qg_s, w_qg_z_profile, graph_state_qg_z_profile, graph_state_joint_qg_s, dicke_qg_z_profile
  • cirq_gate: rqang_gate, full_rqang_gate, signed_rqang_gate, rqang_symbol, append_qang
  • clock_comparison: differential_phase_from_c, ellipse_estimate, moment_estimate, redshift_phase, simulate_pairs
  • complementarity: predictability, visibility, duality_sum, von_neumann_entropy_bits, entropic_sum, entropic_bound, duality_from_counts, entropic_sum_from_counts
  • core: qg_s_from_qg_z, Qang
  • fisher: fisher_theta, fisher_qg, cramer_rao_qg, shift_gradient, indistinguishable_pair, ansatz_states, ansatz_state, tfim_hamiltonian, energy, gradient, full_metric, block_metric, y_basis_circuit, block_metric_from_counts
  • formulation: kron, pauli, rx, ry, rz, phase, clean, conjugate, conserves_weight, z_parity, single_qg_z, hadamard_n, phase_oracle_output, simon_output, grover_state, grover_qg_z_prediction, qft_matrix, local_qg, kickback_control, counting_qg_x, order_finding_output, purity_from_qg, walk_register_mean, qg_values, state_from_qg, apply_gate, gate_table, is_clifford, born_p0, deutsch_jozsa_is_constant, bernstein_vazirani_secret, simon_nonzero_parities, grover_marked_from_signs, count_from_qg_x, hhl_readout, energy_from_qg, maxcut_from_qg, product_kernel, radius2, radius_profile, radius_deficit, sphere_area, meyer_wallach, gate_radius_class, weight_sector_radius, hadamard_test_radius, algorithm_radii, direction_from_qg
  • geometric: state_from_bloch, bloch_from_state, pancharatnam_phase, solid_angle, berry_phase_from_solid_angle, cone_phase_turns, curvature_flux, geometric_phase_qg
  • gradients: jacobian, inverse_jacobian_raw, inverse_jacobian_clipped, inverse_jacobian_tikhonov, pole_damping_factor, qfi_qg, natural_gradient_step_qg, toy_vqe_energy, toy_vqe_grad_theta, GDHistory, run_gradient_descent, benchmark, MultiGDHistory, multi_param_gradient_descent, signed_theta, signed_qg_step, signed_natural_qg_step
  • ibm: WeightPreservationCheck, measured_physical_qubits, readout_errors, readout_inverse_distribution, ibm_qg, estimator_qg, predict_kept_fraction, linear_chains, best_chain, best_layout, plan_shots, fold_two_qubit_gates, zne_qg, qnn_template, qnn_parameter_values, run_qnn, unary_loader, unary_orthogonal, pca_rotation, unary_spectrum, xy_trotter, xy_exact_occupations, occupations, xxz_trotter, xxz_exact_occupations, unary_overlap_circuit, swap_test_circuit, overlap_fidelity, swap_test_fidelity, add_static_zz
  • interop: canonical_counts, qg_z_profile, weight_filter, filtered_qg_z_profile, joint_qg_s, joint_qg_s_se, sampler_qg, qg_z_observables, filtered_observables, estimator_filtered_qg
  • iqm: check_weight, readout_errors, pole_circuits, readout_from_poles, iqm_qg, predict_kept_fraction, best_chain
  • kernels: unary_embedding, exact_kernel, kernel_from_counts, normalize_gram, alignment, kernel_qang_angle
  • knitting: pauli_rotation_cut_gamma, controlled_rotation_cut_gamma, cut_sampling_overhead, total_sampling_overhead
  • mixed: density_from_statevector, mix, is_valid_density_matrix, qg_z_density, purity, von_neumann_entropy, standard_z_povm, is_valid_povm, povm_outcome_probabilities, qg_s_povm, trine_povm
  • multiqubit: product_state, bell_state, ghz_state, partial_trace, per_qubit_qg_z, marginal_qg_s, marginal_von_neumann_entropy, joint_qg_s, shannon_entropy_plugin_bits, shannon_entropy_miller_madow_bits, joint_qg_s_from_counts, qg_correlation, mean_qg_z, mean_qg_z_from_counts
  • neutrino: phase, two_flavour_probability, two_flavour_qg_z, two_flavour_qang_angle, mixing_angle_from_maximum, mixing_angle_std, two_flavour_circuit, pmns, three_flavour_probabilities, three_flavour_circuit, cp_asymmetry, matter_potential, matter_probabilities, matter_trotter_circuit, first_maximum_energy, occupation_profile, collective_mass_hamiltonian, collective_exact, mass_sector_probabilities, collective_trotter_circuit, solar_core_potential, solar_matter_angle, solar_pee_from_p2, solar_pee_adiabatic, solar_slab_edges, solar_slab_unitaries, solar_p2, solar_p2_exact, solar_circuit, pmns_majorana, majorana_invisible, masses, m_bb, majorana_circuit, sterile_angles, sterile_mixing, sterile_probabilities, sterile_circuit
  • pennylane_gate: rqang, full_rqang, append_qang, qg_z_from_probs, kept_fraction, filtered_qg_z
  • phase: QangPhi, anchor_value
  • polarization: stokes_to_qg, qg_to_stokes, degree_of_polarization, purity_from_stokes, jones_to_stokes, jones_to_qg, mueller_from_jones, ptm_from_mueller, mueller_from_ptm, rotator, linear_polarizer, wave_plate, half_wave_plate, quarter_wave_plate, depolarizer, malus_intensity, qg_from_counts
  • postselection: pctc_success, pctc_controlled_qg_z, pctc_circuit, pctc_from_counts, is_scrambler, find_scrambler, yk_decoder_circuit, yk_from_counts
  • probability: readings_from_p0, milliqang_from_p0, p0_from_milliqang, theta_from_milliqang, milliqang_from_theta, angle_per_milliqang, pole_angle, shot_noise_milliqang, shots_for_resolution, pulse_error_milliqang, statistical_angle, Reading, analyze
  • proportions: theta_from_proportion, proportion_from_theta, arcsine, anscombe_theta, theta_variance, proportion_interval, cohens_h, compare_proportions, z_value
  • pulse_area: minimal_area_angle, rx_qg_z_random_amplitude, rx_qg_z_systematic_amplitude, qg_sensitivity, minimal_area_circuit, area
  • qec: encode_bit_flip, extract_syndrome, syndrome_from_qg_z, decode_syndrome, apply_correction, decode_bit_flip
  • qga: QGA_PER_TURN, MILLI_QGA_PER_QGA, FISHER_PER_QGA2, radians_from_qga, qga_from_radians, degrees_from_qga, qga_from_degrees, p0_from_qga, qga_from_p0, milliqang_from_qga, qga_from_milliqang, azimuth_qga, angle_sigma_qga, fubini_study_metric_qga, cone_phase_qga
  • qiskit_gate: RQangGate, FullRQangGate, SignedRQangGate, append_qang, append_rqang_parameter
  • qiskit_ml: loader_inputs, qang_sampler_qnn, qg_features, QangQNNClassifier
  • qml: WeightQNN, MultiClassQNN, kept_fraction, compare_qang
  • qpon: fibre_transmission, link, heralding_probability, singlet_fraction, average_fidelity, optimal_angle, optimal_fidelity, optimal_qg_z, resource_angle_from_qg_z, teleport_circuit, fidelity_from_counts, fidelity_from_correlators, resource_circuit, correlator_from_counts, dual_rail_teleport_circuit, dual_rail_fidelity_from_counts, dual_rail_fidelities
  • qsp: signal_from_qg, qg_of_signal, wqsp_unitary, wqsp_poly, hadamard_test_p0, sample_hadamard_test, fit_phases, wqsp_ops
  • sectors: hamming_weights, filter_distribution, reweight_sectors, sector_exposure, SectorExposurePass, sector_states, echo_transfer_matrix, matrix_power_stochastic, unmix_sector
  • statistics: p0_from_theta, var_qg_z_shot_noise, std_qg_z_shot_noise, propagated_theta_variance, propagated_theta_std, confidence_interval_theta, BootstrapResult, empirical_theta_std, beta_cdf, beta_ppf, QgEstimate, bayes_qg_estimate, wilson_qg_estimate, delta_qg_estimate, qg_estimate, propagated_theta_variance_mixed, theta_qcrb_variance, qg_covariance, delta_method_variance, register_witness_variance, qg_s_from_qg_z_interval, qg_s_estimate, qg2_unbiased, radius2_estimate, direction_estimate
  • transformations: transition_probability_qang
  • varqte: n_params, ansatz, mclachlan_rhs, evolve, xxz_matrix, occupations_from_counts

D.2 qang.integrations

Each submodule imports only its library (Chapter 35); the pip extra is in parentheses.

  • integrations.mitiq (qang[mitiq]): qg_z, filtered_qg_z, qg_executor, execute_with_filter_zne, filter_rule
  • integrations.qiskit_experiments (qang[experiments]): HeraldedReadout, HeraldedReadoutAnalysis, heralded_closed_form, t_eff_from_qg
  • integrations.qiskit_dynamics (qang[dynamics]): rabi_qg, area_error_qg
  • integrations.qutip (qang[qutip]): qg_readings, filtered_qg_z, mesolve_qg, t1_collapse
  • integrations.stim (qang[stim]): detector_qg, observable_qg, measurement_qg, decoded_logical_qg
  • integrations.sklearn (qang[sklearn]): WeightQNNClassifier, MultiClassQNNClassifier
  • integrations.jax (qang[jax]): qg_from_p0, theta_from_qg, milliqang, qg_z_from_probs, filtered_qg_z, pole_damped_update
  • integrations.torch (qang[torch]): WeightQNNTorch, unary_state
  • integrations.qibo (qang[qibo]): rqang, canonical_counts, qg_readout
  • integrations.pytket (qang[pytket]): rqang, qg_readout, statevector_qg
  • integrations.braket (qang[braket]): rqang, run_qg
  • integrations.cudaq (qang[cudaq]): rqang, canonical_counts, qg_readout