tangelo.toolboxes.post_processing package

Subpackages

Submodules

tangelo.toolboxes.post_processing.bootstrapping module

tangelo.toolboxes.post_processing.bootstrapping.get_resampled_frequencies(freq_dict, ncount)

From a frequencies dictionary, makes a set of samples consistent with those frequencies and resample from that set to obtain a new frequencies dictionary consistent with ncount measurements.

Parameters:

• freq_dict (array) – dictionary of measurement/sample frequencies.

• ncount (int) – number of shots/samples to generate resampled frequencies.

Returns

dict: new frequencies dictionary with resampled distribution.

tangelo.toolboxes.post_processing.extrapolation module

tangelo.toolboxes.post_processing.extrapolation.diis(coeffs, energies, stderr=None)

DIIS extrapolation, originally developed by Pulay in Chemical Physics Letters 73, 393-398 (1980)

Parameters:

• coeffs (array-like) – Noise rate amplification factors

• energies (array-like) – Energy expectation values for amplified noise rates

• stderr (array-like, optional) – Energy standard error estimates

Returns:

• float – Extrapolated energy

• float – Error estimation for extrapolated energy

tangelo.toolboxes.post_processing.extrapolation.extrapolation(coeffs, energies, stderr=None, taylor_order=None)

General, DIIS-like extrapolation procedure as found in Nature 567, 491-495 (2019) [arXiv:1805.04492]

Parameters:

• coeffs (array-like) – Noise rate amplification factors

• energies (array-like) – Energy expectation values for amplified noise rates

• stderr (array-like, optional) – Energy standard error estimates

• taylor_order (int, optional) – Taylor expansion order; None for Richardson extrapolation (order determined from number of datapoints), 1 for DIIS extrapolation

Returns:

• float – Extrapolated energy

• float – Error estimation for extrapolated energy

tangelo.toolboxes.post_processing.extrapolation.richardson(coeffs, energies, stderr=None, estimate_exp=False)

General, DIIS-like extrapolation procedure as found in Nature 567, 491-495 (2019) [arXiv:1805.04492]

Parameters:

• coeffs (array-like) – Noise rate amplification factors

• energies (array-like) – Energy expectation values for amplified noise rates

• stderr (array-like, optional) – Energy standard error estimates

• estimate_exp (bool, optional) – Choose to estimate exponent in the Richardson method. Default is False.

Returns:

• float – Extrapolated energy

• float – Error estimation for extrapolated energy

tangelo.toolboxes.post_processing.extrapolation.richardson_analytical(coeffs, energies, stderr=None)

Richardson extrapolation explicit result as found in Phys. Rev. Lett. 119, 180509 [arXiv:1612.02058] (up to sign difference)

Parameters:

• coeffs (array-like) – Noise rate amplification factors

• energies (array-like) – Energy expectation values for amplified noise rates

• stderr (array-like, optional) – Energy standard error estimates

Returns:

• float – Extrapolated energy

• float – Error estimation for extrapolated energy

tangelo.toolboxes.post_processing.extrapolation.richardson_with_exp_estimation(coeffs, energies, stderr=None)

Richardson extrapolation by recurrence, with exponent estimation

Parameters:

• energies (array-like) – Energy expectation values for amplified noise rates

• coeffs (array-like) – Noise rate amplification factors

• stderr (array-like, optional) – Energy standard error estimates

Returns:

• float – Extrapolated energy

• float – Error estimation for extrapolated energy

tangelo.toolboxes.post_processing.histogram module

This module provides a Histogram class and functions to manipulate them, in order to facilitate post-processing of quantum experiments.

class tangelo.toolboxes.post_processing.histogram.Histogram(outcomes, n_shots=0, msq_first=False, epsilon=0.01)

Bases: object

Class to provide useful tools helping redundant tasks when analyzing data from an experiment. The expected data input is an histogram of bitstrings (“010…”), where 0 (resp. 1) correspond to the |0> (resp. |1>) measured state in the computational basis. The outcomes can refer to either the shot counts for each computational basis, or the corresponding probability.

The internal representation is kept as an histogram of shots. Normalized quantities are accessible via the Histogram “frequencies” properties. Bitstrings are stored with the lowest-significant qubit first (lsq_first) ordering.

Parameters:

• string (outcomes (dict of) – int or float): Results in the format of bitstring:

• outcome –

• probability. (where outcome can be a number of shots a) –

• n_shots (int) – Self-explanatory. If it is equal 0, the class considers that probabilities are provided.

• msq_first (bool) – Bit ordering. For example, 011 (msq_first) = 110 (lsq_first). This depends on the hardware provider convention.

• epsilon (float) – When probabilities are provided, this parameter is used to check if the sum is within [1-epsilon, 1+epsilon]. Default is 1e-2.

property frequencies

The frequencies are normalized counts vs the number of shots.

Returns:

dict – Frequencies in a {bitstring: probability, …} format.

get_expectation_value(term, coeff=1.0)

Output the expectation value for qubit operator term. The histogram data is expected to have been acquired in a compatible measurement basis.

Parameters:

• term (openfermion-style QubitOperator object) – a qubit operator, with only a single term.

• coeff (imaginary) – Coefficient to multiply the eigenvalue by.

Returns:

imaginary – Expectation value for this operator.

property n_qubits

The length of the bitstrings represents the number of qubits.”

Returns:

int – Self-explanatory.

property n_shots

Return the number of shots encoded in the Histogram.

Returns:

int – Self-explanatory.

post_select(expected_outcomes)

Method to apply post selection on Histogram data, based on a post selection function in this module. This method changes the Histogram object inplace. This is explicitly done on desired outcomes for specific qubit indices.

Parameters:

expected_outcomes (dict) – Desired outcomes on certain qubit indices and their expected state. For example, {0: “1”, 1: “0”} would filter results based on the first qubit with the |1> state and the second qubit with the |0> state measured.

remove_qubit_indices(*indices)

Method to remove qubit indices in the result. The remaining bitstrings (of new length = length - N_indices) are summed up together.

Parameters:

indices (variable number of int) – Qubit indices to remove.

resample(n_shots)

Generating new Histogram with n_shots, done with the get_resampled_frequencies function (see the relevant documentation for more details).

Parameters:

n_shots (int) – Self-explanatory.

Returns:

Histogram – resampled data with n_shots from the distribution.

tangelo.toolboxes.post_processing.histogram.aggregate_histograms(*hists)

Return a Histogram object formed from data aggregated from all input Histogram objects.

Parameters:

hists (variable number of Histogram objects) – the input Histogram objects.

Returns:

Histogram – The aggregated histogram.

tangelo.toolboxes.post_processing.histogram.filter_hist(hist, function, *args, **kwargs)

Filter selection function to consider bitstrings in respect to a boolean predicate on a bitstring.

Parameters:

• hist (Histogram) – Self-explanatory.

• function (function) – Given a bitstring and some arbitrary arguments, the predicate should return a boolean value.

Returns:

Histogram – New Histogram with filtered outcomes based on the predicate provided.

tangelo.toolboxes.post_processing.mc_weeny_rdm_purification module

tangelo.toolboxes.post_processing.mc_weeny_rdm_purification.mcweeny_purify_2rdm(rdm2_spin, conv=1e-07)

Perform 2-RDM purification based on McWeeny”s algorithm. The value selected for the convergence criteria should be consistent with the accuracy of the 2-RDM provided as input (in particular it should be correlated to the number of shots used to compute the RDM values, if a QPU or a shot-based quantum circuit simulator was used).

This algorithm only works on a RDM associated with a 2-electron system.

Parameters:

• rdm2_spin (numpy array) – The 2-RDM to be purified (in chemistry notation).

• conv (float) – The convergence criteria for McWeeny”s purification.

Returns:

• numpy.array – One-particle RDM in spatial orbital basis.

• numpy.array – Two-particle RDM in spatial orbital basis (in chemistry notation).

tangelo.toolboxes.post_processing.post_selection module

This module provides functions to create symmetry verification and post-selection circuits.

tangelo.toolboxes.post_processing.post_selection.ancilla_symmetry_circuit(circuit, sym_op)

Append a symmetry operator circuit to an input circuit using an extra ancilla qubit, for the purpose of symmetry verification and post-selection. For more details see arXiv:1807.10050.

Parameters:

• circuit (Circuit) – A quantum circuit to be equipped with symmetry verification

• sym_op (string) – The symmetry operator to be verified. Can be a Pauli string, OpenFermion style list or a QubitOperator

Returns:

Circuit – The input circuit appended with the proper basis rotation and entanglement with an ancilla qubit, which is added as the last qubit. This appends an additional qubit to the circuit.

tangelo.toolboxes.post_processing.post_selection.post_select(freqs, expected_outcomes)

Apply post selection to frequency data based on a dictionary of expected outcomes on ancilla qubits.

Parameters:

• freqs (dict) – A dictionary of {bitstring: frequency} pairs

• expected_outcomes (dict) – Desired outcomes on certain qubit indices and their expected state. For example, {0: “1”, 1: “0”} would filter results based on the first qubit with the |1> state and the second qubit with the |0> state measured.

Returns:

dict – A dictionary of post-selected, renormalized frequencies and bitstrings with removed ancilla qubits

tangelo.toolboxes.post_processing.post_selection.split_frequency_dict(frequencies, indices, desired_measurement=None)

Marginalize the frequencies dictionary over the indices. This splits the frequency dictionary into two frequency dictionaries and aggregates the corresponding frequencies. If desired_measurement is provided, the marginalized frequencies are post-selected for that outcome on the mid-circuit measurements.

Parameters:

• frequencies (dict) – The input frequency dictionary

• indices (list) – The list of indices in the frequency dictionary to marginalize over

• desired_measurement (str) – The bit string that is to be selected

Returns:

• dict – The marginal frequencies for provided indices

• dict – The marginal frequencies for remaining indices

tangelo.toolboxes.post_processing.post_selection.split_frequency_dict_for_last_n_digits(frequencies, n)

Marginalize the frequencies dictionary over the last_n_digits. This splits the frequency dictionary into two frequency dictionaries and aggregates the corresponding frequencies.

Parameters:

• frequencies (dict) – The input frequency dictionary

• n (int) – The last n digits of the bitstring to store

Returns:

• dict – The marginal frequencies for remaining indices (different bitstring lengths in general)

• dict – The frequencies for the last n bits

tangelo.toolboxes.post_processing.post_selection.strip_post_selection(freqs, *qubits)

Convenience function to remove the symmetry ancilla qubit and aggregate data to recreate results without post-selection.

Parameters:

• freqs (dict) – A dictionary of {bitstring: frequency} as returned from a quantum device

• qubits (variable number of int) – The ancilla qubit indices to be removed from the bitstrings

Returns:

dict – A frequency dictionary with the qubits stripped and data aggregated

Module contents