AmplitudeEstimation
AmplitudeEstimation(num_eval_qubits, a_factory=None, q_factory=None, i_objective=None, iqft=None, quantum_instance=None)
The Quantum Phase Estimation-based Amplitude Estimation algorithm.
This class implements the original Quantum Amplitude Estimation (QAE) algorithm, introduced by https://arxiv.org/abs/quant-ph/0005055(opens in a new tab). This (original) version uses quantum phase estimation along with a set of m ancilla qubits to find an estimate, that is restricted to the grid
{sin^2(pi y / 2^m) : y = 0, …, 2^{m-1}}.
Using a maximum likelihood post processing, this grid constraint can be circumvented. This improved estimator is implemented as well, see https://arxiv.org/abs/1912.05559(opens in a new tab) Appendix A for more detail.
Parameters
- num_eval_qubits (
int) – Number of evaluation qubits, has a min. value of 1. - a_factory (
Optional[CircuitFactory]) – The CircuitFactory subclass object representing the problem unitary. - q_factory (
Optional[CircuitFactory]) – The CircuitFactory subclass object representing an amplitude estimation sample (based on a_factory). - i_objective (
Optional[int]) – The index of the objective qubit, i.e. the qubit marking ‘good’ solutions with the state |1> and ‘bad’ solutions with the state |0>. - iqft (
Union[QuantumCircuit,IQFT,None]) – The Inverse Quantum Fourier Transform component, defaults to using a standard IQFT when None - quantum_instance (
Union[QuantumInstance,BaseBackend,None]) – Quantum Instance or Backend
Attributes
a_factory
Get the A operator encoding the amplitude a that’s approximated, i.e.
A |0>_n |0> = sqrt{1 - a} |psi_0>_n |0> + sqrt{a} |psi_1>_n |1>
see the original Brassard paper (https://arxiv.org/abs/quant-ph/0005055(opens in a new tab)) for more detail.
Returns
the A operator as CircuitFactory
Return type
backend
i_objective
Get the index of the objective qubit. The objective qubit marks the |psi_0> state (called ‘bad states’ in https://arxiv.org/abs/quant-ph/0005055(opens in a new tab)) with |0> and |psi_1> (‘good’ states) with |1>. If the A operator performs the mapping
A |0>_n |0> = sqrt{1 - a} |psi_0>_n |0> + sqrt{a} |psi_1>_n |1>
then, the objective qubit is the last one (which is either |0> or |1>).
If the objective qubit (i_objective) is not set, we check if the Q operator (q_factory) is set and return the index specified there. If the q_factory is not defined, the index equals the number of qubits of the A operator (a_factory) minus one. If also the a_factory is not set, return None.
Returns
the index of the objective qubit
Return type
int
q_factory
Get the Q operator, or Grover-operator for the Amplitude Estimation algorithm, i.e.
Q = -A S_0 A^{-1} S_psi0,
where S_0 reflects about the |0>_n state and S_psi0 reflects about |psi_0>_n. See https://arxiv.org/abs/quant-ph/0005055(opens in a new tab) for more detail.
If the Q operator is not set, we try to build it from the A operator. If neither the A operator is set, None is returned.
Returns
returns the current Q factory of the algorithm
Return type
QFactory
quantum_instance
Union[None, qiskit.aqua.quantum_instance.QuantumInstance]
Returns quantum instance.
Return type
Optional[QuantumInstance]
random
Return a numpy random.
Methods
confidence_interval
AmplitudeEstimation.confidence_interval(alpha, kind='likelihood_ratio')
Compute the (1 - alpha) confidence interval.
Parameters
- alpha (
float) – Confidence level: compute the (1 - alpha) confidence interval. - kind (
str) – The method to compute the confidence interval, can be ‘fisher’, ‘observed_fisher’ or ‘likelihood_ratio’ (default)
Return type
List[float]
Returns
The (1 - alpha) confidence interval of the specified kind.
Raises
- AquaError – If ‘mle’ is not in self._ret.keys() (i.e. run was not called yet).
- NotImplementedError – If the confidence interval method kind is not implemented.
construct_circuit
AmplitudeEstimation.construct_circuit(measurement=False)
Construct the Amplitude Estimation quantum circuit.
Parameters
measurement (bool) – Boolean flag to indicate if measurements should be included in the circuit.
Return type
Returns
The QuantumCircuit object for the constructed circuit.
run
AmplitudeEstimation.run(quantum_instance=None, **kwargs)
Execute the algorithm with selected backend.
Parameters
- quantum_instance (
Union[QuantumInstance,BaseBackend,None]) – the experimental setting. - kwargs (dict) – kwargs
Returns
results of an algorithm.
Return type
dict
Raises
AquaError – If a quantum instance or backend has not been provided
set_backend
AmplitudeEstimation.set_backend(backend, **kwargs)
Sets backend with configuration.
Return type
None