2.1.4. filter_functions.numeric

This module defines the functions to calculate everything related to filter functions.

2.1.4.1. Functions

calculate_control_matrix_from_atomic(): Calculate the control matrix from those of atomic pulse sequences
calculate_control_matrix_from_scratch(): Calculate the control matrix from scratch
calculate_control_matrix_periodic(): Calculate the control matrix for a periodic Hamiltonian
calculate_noise_operators_from_atomic(): Calculate the interaction picture noise operators from atomic segments. Same calculation as calculate_control_matrix_from_atomic() except in Hilbert space.
calculate_noise_operators_from_scratch(): Calculate the interaction picture noise operators from scratch. Same calculation as calculate_control_matrix_from_scratch() except in Hilbert space.
calculate_cumulant_function(): Calculate the cumulant function for a given PulseSequence object.
calculate_decay_amplitudes(): Calculate the decay amplitudes, corresponding to first order terms of the Magnus expansion
calculate_frequency_shifts(): Calculate the frequency shifts, corresponding to second order terms of the Magnus expansion
calculate_filter_function(): Calculate the filter function from the control matrix
calculate_second_order_filter_function(): Calculate the second order filter function used to compute the frequency shifts.
calculate_pulse_correlation_filter_function(): Calculate the pulse correlation filter function from the control matrix
diagonalize(): Diagonalize a Hamiltonian
error_transfer_matrix(): Calculate the error transfer matrix of a pulse up to a unitary rotation
infidelity(): Function to compute the infidelity of a pulse defined by a PulseSequence instance for a given noise spectral density and frequencies

Functions

`calculate_control_matrix_from_atomic`(phases, ...)	Calculate the control matrix from the control matrices of atomic segments.
`calculate_control_matrix_from_scratch`(...[, ...])	Calculate the control matrix from scratch, i.e. without knowledge of the control matrices of more atomic pulse sequences.
`calculate_control_matrix_periodic`(phases, ...)	Calculate the control matrix of a periodic pulse given the phase factors, control matrix and transfer matrix of the total propagator, total_propagator_liouville, of the atomic pulse.
`calculate_cumulant_function`(pulse[, ...])	Calculate the cumulant function \(\mathcal{K}(\tau)\).
`calculate_decay_amplitudes`(pulse, spectrum, ...)	Get the decay amplitudes \(\Gamma_{\alpha\beta, kl}\) for noise sources \(\alpha,\beta\) and basis elements \(k,l\).
`calculate_filter_function`(control_matrix[, ...])	Compute the filter function from the control matrix.
`calculate_frequency_shifts`(pulse, spectrum, ...)	Get the frequency shifts \(\Delta_{\alpha\beta, kl}\) for noise sources \(\alpha,\beta\) and basis elements \(k,l\).
`calculate_noise_operators_from_atomic`(...[, ...])	Calculate the interaction picutre noise operators from atomic segments.
`calculate_noise_operators_from_scratch`(...)	Calculate the noise operators in interaction picture from scratch.
`calculate_pulse_correlation_filter_function`(...)	Compute pulse correlation filter function from control matrix.
`calculate_second_order_filter_function_from_atomic`(...)	Calculate the second-order filter function from those of atomic segments.
`calculate_second_order_filter_function_from_scratch`(...)	Calculate the second order filter function for frequency shifts.
`diagonalize`(hamiltonian, dt)	Diagonalize a Hamiltonian.
`error_transfer_matrix`([pulse, spectrum, ...])	Compute the error transfer matrix up to unitary rotations.
`infidelity`(pulse, spectrum, omega[, ...])	Calculate the leading order entanglement infidelity.