POVMPostProcessor

class POVMPostProcessor(povm_sample: POVMPubResult, dual: BaseDual | None = None)

Bases: object

The canonical POVM result post-processor.

This post-processor implementation provides a straight-forward interface for computing the expectation values (and standard deviations) of any Pauli-based observable. It is initialized with a POVMPubResult as shown below:

>>> from povm_toolbox.library import ClassicalShadows
>>> from povm_toolbox.sampler import POVMSampler
>>> from povm_toolbox.post_processor import POVMPostProcessor
>>> from qiskit.circuit import QuantumCircuit
>>> from qiskit.primitives import StatevectorSampler
>>> from qiskit.quantum_info import SparsePauliOp
>>> circ = QuantumCircuit(2)
>>> _ = circ.h(0)
>>> _ = circ.cx(0, 1)
>>> povm = ClassicalShadows(2, seed=42)
>>> sampler = StatevectorSampler(seed=42)
>>> povm_sampler = POVMSampler(sampler)
>>> job = povm_sampler.run([circ], povm=povm, shots=16)
>>> result = job.result()
>>> post_processor = POVMPostProcessor(result[0])
>>> post_processor.get_expectation_value(SparsePauliOp("ZI"))  
(-0.75, 0.33541019662496846)

Additionally, this post-processor also supports the customization of the Dual frame in which the decomposition weights of the provided observable are obtained. Check out this how-to guide for more details on how to do this.

Initialize the POVM post-processor.

Parameters:

• povm_sample (POVMPubResult) – a result from a POVM sampler run.

• dual (BaseDual | None) – the Dual frame that will be used to obtain the decomposition weights of an observable when computing its expectation value. For more details, refer to get_decomposition_weights(). When this is None, the standard “state-average” Dual frame will be constructed from the POVM stored in the povm_sample’s POVMPubResult.metadata.

Raises:

ValueError – If the provided dual is not a dual frame to the POVM stored in the povm_samples’s POVMPubResult.metadata.

Attributes

counts

Return the histogram of the POVM outcomes via POVMPubResult.get_counts().

dual

Return the Dual frame that is used.

Warning

If the dual frame is not already built, accessing this property could be computationally demanding.

povm

Return the POVM definition that was used to sample outcomes.

Methods

get_decomposition_weights(observable: SparsePauliOp, outcome_set: set[Any]) → dict[Any, float]

Get the decomposition weights of observable into the elements of povm.

Given an observable \(O\) which is in the span of a POVM (here, povm), one can write \(O\) as the weighted sum of the POVM effects, \(O = \sum_k w_k M_k\) for real weights \(w_k\) and where \(k\) labels the outcomes.

See also BaseDual.get_omegas().

Parameters:

• observable (SparsePauliOp) – the observable to be decomposed into the POVM effects.

• outcome_set (set[Any]) – set of outcome labels indicating which decomposition weights are queried. An outcome of a ProductPOVM is labeled by a tuple of integers for instance. For a MultiQubitPOVM, an outcome is simply labeled by an integer.

Returns:

A dictionary mapping outcome labels to decomposition weights.

Return type:

dict[Any, float]

get_expectation_value(observable: SparsePauliOp, *, loc: int | tuple[int, ...] | None = None) → tuple[ndarray, ndarray] | tuple[float, float]

Return the expectation value and standard deviation of the given observable.

Parameters:

• observable (SparsePauliOp) – the observable whose expectation value is queried.

• loc (int | tuple[int, ...] | None) – this argument is relevant if multiple sets of parameter values were supplied to the sampler in the same POVMSamplerPub. The index loc then corresponds to the set of parameter values that was supplied to the sampler through the Pub. If None, the expectation value (and standard deviation) for each set of circuit parameters is returned.

Returns:

A tuple of (estimated) expectation value(s) and standard deviation(s). If a single value was queried (via loc), both of these will be a float. Otherwise, they will be instances of numpy.ndarray.

Return type:

tuple[ndarray, ndarray] | tuple[float, float]