PEA

Default value: '0.2'

static compute_expectation_value(item_result, observables, param_shape=None, param_basis_pairs=None, meas_bases=None, broadcast_obs_and_params=False, measure_noise_data=None, meas_qubits=None, circuit_num_qubits=None)

Process expectation values for a single item result.

This function can be used to calculate expectation values for a single unmitigated item result without instantiating a new class instance.

Parameters

• item_result (QuantumProgramItemResult) – The item result.
• observables (ObservablesArray |Sequence[SparsePauliOp]) – The observables to calculate expectation values for.
• param_shape (tuple[int, ...] | None) – The shape of the parameter values.
• param_basis_pairs (list[tuple[tuple[int, ...], str]] | None) – The map between params ndindexes to measure basis.
• meas_bases (Sequence[Pauli] | Sequence[str] | PauliList | None) – A list of the measured Pauli bases. The i th item is a measurement basis assumed to correspond to the i th slice of the data in item_result.
• broadcast_obs_and_params (bool) – Whether to broadcast observables and parameter values.
• measure_noise_data (PauliLindbladMap |ndarray | None) – Measurement noise calibration data for TREX mitigation.
• meas_qubits (list[int] | None) – Sorted list of the circuit qubit indices that were measured, if the task was prepared with trim_measurements=True (available as task.meas_qubits). Must be given together with circuit_num_qubits. If None, all the qubits are assumed to be measured, which gives wrong results for trimmed data.
• circuit_num_qubits (int | None) – The total number of qubits in the circuit. Used together with meas_qubits to expand the data back to the full width. Must be given together with meas_qubits.

Returns

A PubResult which contains evs and std as fields in its data, where evs are expectation values, and std are the standard deviation of the expectation values. If broadcast_obs_and_params is set to True, the data will contain also a twirl_stds field which is the standard deviation between different randomizations.

Raises

• ValueError – If item_result has no '_meas' key.
• ValueError – If item_result['_meas'] has invalid number of axes.
• ValueError – If param_shape and observables.shape cannot be broadcasted against each other.
• ValueError – If only one of meas_qubits and circuit_num_qubits is given.

Return type

PubResult

static compute_expectation_value_pea(item_result, observables, param_shape, param_basis_pairs, noise_factors, extrapolator, extrapolated_noise_factors=None, meas_bases=None, broadcast_obs_and_params=False, measure_noise_data=None, custom_fit=None, meas_qubits=None, circuit_num_qubits=None)

Process expectation values for a single item result.

This function can be used to calculate expectation values for a single pea mitigated item result without instantiating a new class instance.

Parameters

• item_result (QuantumProgramItemResult) – The pea mitigated item result.

• observables (ObservablesArray |Sequence[SparsePauliOp]) – The observables to calculate expectation values for.

• param_shape (tuple[int, ...] | None) – The shape of the parameter values.

• param_basis_pairs (list[tuple[tuple[int, ...], str]] | None) – The map between params ndindexes to measure basis.

• noise_factors (list[float]) – The noise factors that were used to amplify the noise.

• extrapolated_noise_factors (float |int |list[float] | None) – Noise factors to evaluate the fits at.

• extrapolator (list[Literal['linear', 'exponential', 'double_exponential', 'polynomial_degree_1', 'polynomial_degree_2', 'polynomial_degree_3', 'polynomial_degree_4', 'polynomial_degree_5', 'polynomial_degree_6', 'polynomial_degree_7', 'fallback', 'custom']]) –

  The extrapolator model or models to use. Models will be tried in priority order. Supported models (each fits the named function of the noise factor x):

  • "linear": a + b*x
  • "polynomial_degree_k" (1 <= k <= 7): a degree-k polynomial
  • "exponential": a*exp(b*x)
  • "double_exponential": a*exp(b*x) + c*exp(d*x) (rates constrained to decay)
  • "fallback": no fit; the measured value at the lowest noise factor
  • custom: The custom extrapolation function given in custom_fit parameter

• meas_bases (Sequence[Pauli] | Sequence[str] | PauliList | None) – A list of the measured Pauli bases. The i th item is a measurement basis assumed to correspond to the i th slice of the data in item_result.

• broadcast_obs_and_params (bool) – Whether to broadcast observables and parameter values.

• measure_noise_data (PauliLindbladMap |ndarray | None) – Measurement noise calibration data for TREX mitigation. Can be either a PauliLindbladMap of a noise model learned upfront, or a result of a calibration circuit.

• custom_fit (tuple[Callable[[...], ndarray], list[float], tuple[float, ...] | tuple[list[float], ...]] | None) – A custom fitting function that will be used for extrapolation. Should include a tuple in the form of: (function, p_0, bounds). The function should take the independent variable as the first argument and the parameters to fit as separate remaining arguments. p_0 is an array of the initial guess for the parameters, and bounds are the bounds on the parameters. These parameters will be sent as arguments for scipy.optimize.curve_fit function.

• meas_qubits (list[int] | None) – Sorted list of the circuit qubit indices that were measured, if the task was prepared with trim_measurements=True (available as task.meas_qubits). Must be given together with circuit_num_qubits. If None, all the qubits are assumed to be measured, which gives wrong results for trimmed data.

• circuit_num_qubits (int | None) – The total number of qubits in the circuit. Used together with meas_qubits to expand the data back to the full width. Must be given together with meas_qubits.

Returns

• evs: expectation values evaluated at the zero noise point.

• std: the standard deviations of the extrapolated expectation values evaluated at the zero noise point.

• evs_noise_factors: expectation values calculated at the noise_factors points.

• stds_noise_factors: standard deviations calculated at the noise_factors points.

• stds_twirl_noise_factors: standard deviations between different randomizations calculated at the

  noise_factors points.

• evs_extrapolated: expectation values evaluated at the extrapolated_noise_factors points.

  Set to None if extrapolated_noise_factors is None.

• stds_extrapolated: standard deviations calculated at the extrapolated_noise_factors points.

  Set to None if extrapolated_noise_factors is None.

The PubResult will also contain a selected_extrapolators field in the metadata, which is the valid extrapolators used to extrapolate the data for each observable term for the zero noise extrapolation point.

Return type

A PubResult which contains the following fields

Raises

• ValueError – If item_result has no '_meas' key.
• ValueError – If item_result['_meas'] has invalid number of axes.
• ValueError – If param_shape and observables.shape cannot be broadcasted against each other.
• ValueError – If noise_factors is under-specified for any extrapolator.
• ValueError – If only one of meas_qubits and circuit_num_qubits is given.

static create_instance_from_passthrough_data(passthrough, trex=None)

Create a PEA instance from a passthrough dictionary loaded from a quantum program execution result.

Parameters

• passthrough (dict[str, Any]) – Passthrough_data dictionary loaded from a quantum program execution result.
• trex (TREX | None) – A TREX instance containing a calibration circuit results executed in the same quantum program. Should remain None in case TREX mitigation was not used or a TREX calibration was not executed as part of thq same quantum program.

Returns

A PEA instance.

Return type

PEA

find_unique_layers(circuit, custom_boxing_options=None, box_types='all', observables=None, trex=None)

Return the unique boxed layers of the given circuit using the given boxing options.

If the instance already holds a boxed circuit of the given circuit (for example, after calling prepare), and custom_boxing_options is None or equal to the saved boxing options, the saved boxed circuit is used instead of boxing the circuit again.

Parameters

• circuit (QuantumCircuit) – The circuit to found its unique layers.

• custom_boxing_options (dict | None) – The custom boxing options that will be used by generate_boxing_pass_manager() function.

• box_types (Literal['gates', 'measurement', 'all']) – Can be either "gates", "measurement" or "all", corresponding to filter boxes with only gate layers, only measurement layers or all layers, respectively.

• observables (ObservablesArray |Sequence[SparsePauliOp] | None) –

  If given, the layers are found for a circuit whose measurements are trimmed to the active and observed qubits, exactly as when prepare is called with trim_measurements=True and the same observables. If None (default), all the qubits are measured.

  Warning

  Pass observables if and only if trim_measurements=True is passed to prepare, together with the same observables. The measured qubits change the boxing, so layers learned with a different choice are not found by prepare.

• trex (bool | None) – Whether to add the boxing options that prepare enforces when a TREX is used (measurement boxes annotated for all qubits). If True, these options are always added. If False, they are never added. If None (default), they are added if and only if this task has a TREX mitigation.

Returns

Unique boxed layers of the given circuit.

Raises

ValueError – If observables is given and no qubit is active or observed.

Return type

list[CircuitInstruction]

postprocess(results, measure_noise_data=None, *, noise_factors=None, extrapolator=None, extrapolated_noise_factors=None, custom_fit=None)

Process expectation values for a single item result.

Parameters

• results (QuantumProgramItemResult |QuantumProgramResult) – The execution results. Can be either the entire results object or the pea mitigated item result of this task. If TREX calibration task is added to the quantum program, its results will be used to compute the measure noise data if the entire results object is provided.

• noise_factors (Sequence[float] | None) – The noise factors that were used to amplify the noise.

• extrapolated_noise_factors (list[float] | None) – Noise factors to evaluate the fits at.

• extrapolator (Sequence[Literal['linear', 'exponential', 'double_exponential', 'polynomial_degree_1', 'polynomial_degree_2', 'polynomial_degree_3', 'polynomial_degree_4', 'polynomial_degree_5', 'polynomial_degree_6', 'polynomial_degree_7', 'fallback', 'custom']] | None) –

  The extrapolator model or models to use. Models will be tried in priority order. Supported models (each fits the named function of the noise factor x):

  • "linear": a + b*x
  • "polynomial_degree_k" (1 <= k <= 7): a degree-k polynomial
  • "exponential": a*exp(b*x)
  • "double_exponential": a*exp(b*x) + c*exp(d*x) (rates constrained to decay)
  • "fallback": no fit; the measured value at the lowest noise factor
  • custom: The custom extrapolation function given in custom_fit parameter

• measure_noise_data (PauliLindbladMap |ndarray | None) – Measurement noise calibration data for TREX mitigation. Can be either a PauliLindbladMap of a noise model learned upfront, or a result of a calibration circuit.

• custom_fit (tuple[Callable[[...], ndarray], list[float], tuple[float, ...] | tuple[list[float], ...]] | None) – A custom fitting function that will be used for extrapolation. Should include a tuple in the form of: (function, p_0, bounds). The function should take the independent variable as the first argument and the parameters to fit as separate remaining arguments. p_0 is an array of the initial guess for the parameters, and bounds are the bounds on the parameters. These parameters will be sent as arguments for scipy.optimize.curve_fit function.

Returns

• evs: expectation values evaluated at the zero noise point.

• std: the standard deviations of the extrapolated expectation values evaluated at the zero noise point.

• evs_noise_factors: expectation values calculated at the noise_factors points.

• stds_noise_factors: standard deviations calculated at the noise_factors points.

• stds_twirl_noise_factors: standard deviations between different randomizations calculated at the

  noise_factors points.

• evs_extrapolated: expectation values evaluated at the extrapolated_noise_factors points.

  Set to None if extrapolated_noise_factors is None.

• stds_extrapolated: standard deviations calculated at the extrapolated_noise_factors points.

  Set to None if extrapolated_noise_factors is None.

The PubResult will also contain a selected_extrapolators field in the metadata, which is the valid extrapolators used to extrapolate the data for each observable term for the zero noise extrapolation point.

Return type

A PubResult which contains the following fields

Raises

• ValueError – If the task’s item result has no '_meas' key.
• ValueError – If the item result’s '_meas' data has an invalid number of axes.
• ValueError – If param_shape and observables.shape cannot be broadcasted against each other.

prepare(circuit, observables, parameters, custom_boxing_options=None, shots_per_randomization=64, num_randomizations=128, broadcast_obs_and_params=False, trex=None, quantum_program=None, trim_measurements=False, *, noise_maps=None, noise_factors=(1, 3, 5), extrapolator=None, extrapolated_noise_factors=None)

Creates a QuantumProgram with PEA mitigated item for executing via Executor.

Creates an item for a QuantumProgram, that can be executed via Executor and is PEA mitigated (amplifies the noise by scaling the injected Pauli noise and extrapolates to the zero noise point). If a quantum_program is provided, the new item will be added to the existing program, otherwise, a new program will be created, containing only the created item. In the created program item the final measurement layer of the given circuit is removed and a new measurement layer with a dedicated classical register named _meas is added. If broadcast_obs_and_params is True, the observables and parameters will be broadcasted using the samplomatic broadcasting rules, to allow attaching some of the parameters to some of the observables. Otherwise, every parameter will be executed for each observable (outer product of the parameters and observables). Note that the post-processing of an outer product is usually faster.

Parameters

• circuit (QuantumCircuit) – The quantum circuit.

• observables (ObservablesArray |Sequence[SparsePauliOp]) – The observables to calculate their expectation values.

• parameters (ndarray | None) – The parameters of a parametric circuit.

• custom_boxing_options (dict | None) – The custom boxing options that will be used by generate_boxing_pass_manager() function.

• shots_per_randomization (int) – The number of shots per randomization.

• num_randomizations (int) – The number of randomizations.

• broadcast_obs_and_params (bool) – Whether to broadcast observables and parameters.

• trex (TREX | None) – A TREX mitigation instance that will be used to mitigate readout errors.

• quantum_program (QuantumProgram | None) – The quantum program to add an item for. If None, a new program will be created.

• trim_measurements (bool) –

  Whether to measure only the qubits that have instructions on them or are in the support of the observables, instead of all the qubits of the circuit. The measured qubits are available in meas_qubits after the call.

  Warning

  Trimming changes the boxing of the circuit, so noise_maps must be learned on the layers of a trimmed circuit: pass observables to the layer finder (find_combined_unique_layers() or find_unique_layers()) if and only if trim_measurements=True is passed to prepare, and pass the same observables.

• noise_maps (dict[str, PauliLindbladMap] | None) – A mapping between layer ref to a noise model to use for noise amplification. The dict might contain layers not present in the given circuit, but must contain all the mitigated layers. Assumes that the unique layers used for noise learning were extracted using the find_unique_layers method with the same custom boxing options, and with observables passed if and only if trim_measurements=True.

• noise_factors (Sequence[float |int]) – The noise factors to use for amplifying the noise.

• extrapolator (Sequence[Literal['linear', 'exponential', 'double_exponential', 'polynomial_degree_1', 'polynomial_degree_2', 'polynomial_degree_3', 'polynomial_degree_4', 'polynomial_degree_5', 'polynomial_degree_6', 'polynomial_degree_7', 'fallback', 'custom']] | None) –

  The extrapolator model or models planned to be used in post-processing. Used in preparation to validate that enough noise factors are present for a valid fit using these extrapolators. If None, not validation will be done. Supported models (each fits the named function of the noise factor x):

  • "linear": a + b*x
  • "polynomial_degree_k" (1 <= k <= 7): a degree-k polynomial
  • "exponential": a*exp(b*x)
  • "double_exponential": a*exp(b*x) + c*exp(d*x) (rates constrained to decay)
  • "fallback": no fit; the measured value at the lowest noise factor

• extrapolated_noise_factors (list[float] | None) – The noise factors to evaluate the fits at planned to be used in post-processing. Used for saving the data for easy post-processing. Can be overwritten in the post-processing.

Returns

A QuantumProgram with PEA mitigated item that can be executed via Executor.

Raises

ValueError – If trim_measurements is True and no qubit is active or observed.

Return type

QuantumProgram