---
title: OBPMetadata (latest version)
description: API reference for qiskit_addon_obp.utils.metadata.OBPMetadata in the latest version of qiskit-addon-obp
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit-addon-obp/utils-metadata-obp-metadata
---

# OBPMetadata

*class* `OBPMetadata(truncation_error_budget, num_slices, operator_budget, backpropagation_history, num_backpropagated_slices)`

[GitHub](https://github.com/Qiskit/qiskit-addon-obp/tree/main/qiskit_addon_obp/utils/metadata.py#L93-L259)

Bases: [`object`](https://docs.python.org/3/library/functions.html#object)

A container for metadata generated during the `backpropagate()` method.

## Attributes

**Parameters**

- **truncation\_error\_budget** ([*TruncationErrorBudget*](/docs/api/qiskit-addon-obp/utils-truncating#truncationerrorbudget "qiskit_addon_obp.utils.truncating.TruncationErrorBudget"))
- **num\_slices** ([*int*](https://docs.python.org/3/library/functions.html#int) *| None*)
- **operator\_budget** ([*OperatorBudget*](/docs/api/qiskit-addon-obp/utils-simplify#operatorbudget "qiskit_addon_obp.utils.simplify.OperatorBudget"))
- **backpropagation\_history** ([*list*](https://docs.python.org/3/library/stdtypes.html#list)*\[*[*SliceMetadata*](/docs/api/qiskit-addon-obp/utils-metadata-slice-metadata "qiskit_addon_obp.utils.metadata.SliceMetadata")*]*)
- **num\_backpropagated\_slices** ([*int*](https://docs.python.org/3/library/functions.html#int))

### truncation\_error\_budget

Type: [`TruncationErrorBudget`](/docs/api/qiskit-addon-obp/utils-truncating#truncationerrorbudget "qiskit_addon_obp.utils.truncating.TruncationErrorBudget")

Values specifying the observable truncation strategy.

### num\_slices

Type: [`int`](https://docs.python.org/3/library/functions.html#int) | [`None`](https://docs.python.org/3/library/constants.html#None)

The total number of slices to attempt to backpropagate.

### operator\_budget

Type: [`OperatorBudget`](/docs/api/qiskit-addon-obp/utils-simplify#operatorbudget "qiskit_addon_obp.utils.simplify.OperatorBudget")

Values specifying how large the operator may grow.

### backpropagation\_history

Type: [`list`](https://docs.python.org/3/library/stdtypes.html#list)\[[`SliceMetadata`](/docs/api/qiskit-addon-obp/utils-metadata-slice-metadata "qiskit_addon_obp.utils.metadata.SliceMetadata")]

A sequence of metadata objects to track the progression of the backpropagation.

### num\_backpropagated\_slices

Type: [`int`](https://docs.python.org/3/library/functions.html#int)

The number of backpropagated slices.

> **Note**
>
> This value can differ from `len(backpropagation_history)` in cases where a stopping criterion such as `operator_budget.max_paulis` or `operator_budget.max_qwc_groups` caused the backpropagation to terminate. Then, this value should be equal to `len(backpropagation_history) - 1` because the last slice caused the thresholds to be exceeded. However, for convenience these values are still recorded for the end-user to inspect them.

## Methods

### accumulated\_error

`accumulated_error(observable_idx, slice_idx=None)`

[GitHub](https://github.com/Qiskit/qiskit-addon-obp/tree/main/qiskit_addon_obp/utils/metadata.py#L121-L159)

Compute the accumulated error for a given observable at a given “time”.

This method computes the accumulated error for a given observable index at a given “time” during the course of the backpropagation. In this context, “time” is to be understood as the discrete steps of already backpropagated slices.

The accumulated error is computed as the sum of the individual [`SliceMetadata.slice_errors`](/docs/api/qiskit-addon-obp/utils-metadata-slice-metadata#slice_errors "qiskit_addon_obp.utils.metadata.SliceMetadata.slice_errors"). These in turn may be computed within a specified [`TruncationErrorBudget.p_norm`](/docs/api/qiskit-addon-obp/utils-truncating#p_norm "qiskit_addon_obp.utils.truncating.TruncationErrorBudget.p_norm"). Thus, the computed accumulated error is an upper bound to the real accumulated error as given by the [Minkowski inequality](https://en.wikipedia.org/wiki/Minkowski_inequality) (the generalization of the triangle inequality for Lp-norms other than `p=2`).

> **Note**
>
> Since a general Lp-norm (other than `p=2`) is *not* an inner product norm, it does *not* satisfy the [parallelogram law](https://en.wikipedia.org/wiki/Parallelogram_law). Hence, we must use the Minkowski inequality as the upper bound of the accumulated error.

**Parameters**

- **observable\_idx** ([*int*](https://docs.python.org/3/library/functions.html#int)) – the index of the observable whose accumulated error to compute.
- **slice\_idx** ([*int*](https://docs.python.org/3/library/functions.html#int) *| None*) – the index of the slice (the discrete “time” step) up to which to compute the accumulated error. If this is `None`, it will default to `self.num_backpropagated_slices` which is equivalent to computing the accumulated error of an observable at the latest point in time which has not surpassed any stopping criteria in the algorithm

**Returns**

The accumulated error computed per the explanations above.

**Return type**

[float](https://docs.python.org/3/library/functions.html#float)

### from\_json

*classmethod* `from_json(json_file)`

[GitHub](https://github.com/Qiskit/qiskit-addon-obp/tree/main/qiskit_addon_obp/utils/metadata.py#L224-L248)

Load a metadata from a json file.

**Parameters**

**json\_file** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – the path to the file to be loaded.

**Returns**

The loaded metadata.

**Return type**

[*OBPMetadata*](#qiskit_addon_obp.utils.metadata.OBPMetadata "qiskit_addon_obp.utils.metadata.OBPMetadata")

### left\_over\_error\_budget

`left_over_error_budget(observable_idx, slice_idx=None)`

[GitHub](https://github.com/Qiskit/qiskit-addon-obp/tree/main/qiskit_addon_obp/utils/metadata.py#L161-L222)

Compute the left-over error budget for a given observable at a given “time”.

This method computes the left-over error budget for a given observable index at a given “time” during the course of the backpropagation. In this context, “time” is to be understood as the discrete steps of already backpropagated slices.

The left-over error budget is computed as the remainder of the total budget minus the sum of the individual [`SliceMetadata.slice_errors`](/docs/api/qiskit-addon-obp/utils-metadata-slice-metadata#slice_errors "qiskit_addon_obp.utils.metadata.SliceMetadata.slice_errors"). These in turn may be computed within a specified [`TruncationErrorBudget.p_norm`](/docs/api/qiskit-addon-obp/utils-truncating#p_norm "qiskit_addon_obp.utils.truncating.TruncationErrorBudget.p_norm").

> **Note**
>
> See also the explanations in [`accumulated_error()`](#qiskit_addon_obp.utils.metadata.OBPMetadata.accumulated_error "qiskit_addon_obp.utils.metadata.OBPMetadata.accumulated_error") for more details on how the individual slice errors are summed up to form an upper bound to the real error via the Minkowski inequality.

> **Note**
>
> The left-over error budget is relative to the value of `self.truncation_error_budget.max_error_total` which may be `numpy.inf` in which case the returned value of this method will be `numpy.inf`, too.

**Parameters**

- **observable\_idx** ([*int*](https://docs.python.org/3/library/functions.html#int)) – the index of the observable whose left-over error budget to compute.
- **slice\_idx** ([*int*](https://docs.python.org/3/library/functions.html#int) *| None*) – the index of the slice (the discrete “time” step) up to which to compute the left-over error budget. If this is `None`, it will default to `self.num_backpropagated_slices` which is equivalent to computing the left-over error budget of an observable at the latest point in time which has not surpassed any stopping criteria in the algorithm

**Returns**

The left-over error budget computed per the explanations above.

**Return type**

[float](https://docs.python.org/3/library/functions.html#float)

### to\_json

`to_json(json_file, **kwargs)`

[GitHub](https://github.com/Qiskit/qiskit-addon-obp/tree/main/qiskit_addon_obp/utils/metadata.py#L250-L259)

Dump this metadata to a json file.

**Parameters**

- **json\_file** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – the path to the file into which to dump the metadata.
- **kwargs** – keyword arguments to be passed on towards `json.dump()`.

**Return type**

None