IterativeAmplitudeEstimation
IterativeAmplitudeEstimation(epsilon, alpha, confint_method='beta', min_ratio=2, a_factory=None, q_factory=None, i_objective=None, quantum_instance=None)
The Iterative Amplitude Estimation algorithm.
This class implements the Iterative Quantum Amplitude Estimation (QAE) algorithm, proposed in https://arxiv.org/abs/1912.05559(opens in a new tab). The output of the algorithm is an estimate that, with at least probability 1 - alpha, differs by epsilon to the target value, where both alpha and epsilon can be specified.
It differs from the original QAE algorithm proposed by Brassard (https://arxiv.org/abs/quant-ph/0005055(opens in a new tab)) in that it does not rely on Quantum Phase Estimation, but is only based on Grover’s algorithm. Iterative IQAE iteratively applies carefully selected Grover iterations to find an estimate for the target amplitude.
The output of the algorithm is an estimate for the amplitude a, that with at least probability 1 - alpha has an error of epsilon. The number of A operator calls scales linearly in 1/epsilon (up to a logarithmic factor).
Parameters
- epsilon (
float) – Target precision for estimation target a, has values between 0 and 0.5 - alpha (
float) – Confidence level, the target probability is 1 - alpha, has values between 0 and 1 - confint_method (
str) – Statistical method used to estimate the confidence intervals in each iteration, can be ‘chernoff’ for the Chernoff intervals or ‘beta’ for the Clopper-Pearson intervals (default) - min_ratio (
float) – Minimal q-ratio (K_{i+1} / K_i) for FindNextK - a_factory (
Optional[CircuitFactory]) – The A operator, specifying the QAE problem - q_factory (
Optional[CircuitFactory]) – The Q operator (Grover operator), constructed from the A operator - i_objective (
Optional[int]) – Index of the objective qubit, that marks the ‘good/bad’ states - quantum_instance (
Union[QuantumInstance,BaseBackend,None]) – Quantum Instance or Backend
Raises
AquaError – if the method to compute the confidence intervals is not supported
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
precision
float
Returns the target precision epsilon of the algorithm.
Return type
float
Returns
The target precision (which is half the width of the confidence interval).
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
construct_circuit
IterativeAmplitudeEstimation.construct_circuit(k, measurement=False)
Construct the circuit Q^k A |0>.
The A operator is the unitary specifying the QAE problem and Q the associated Grover operator.
Parameters
- k (
int) – The power of the Q operator. - measurement (
bool) – Boolean flag to indicate if measurements should be included in the circuits.
Return type
Returns
The circuit Q^k A |0>.
run
IterativeAmplitudeEstimation.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
IterativeAmplitudeEstimation.set_backend(backend, **kwargs)
Sets backend with configuration.
Return type
None