qiskit.aqua.algorithms.IterativeAmplitudeEstimation

__init__(epsilon, alpha, confint_method='beta', min_ratio=2, state_preparation=None, grover_operator=None, objective_qubits=None, post_processing=None, a_factory=None, q_factory=None, i_objective=None, initial_state=None, quantum_instance=None)

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
• state_preparation (Union[QuantumCircuit, CircuitFactory, None]) – A circuit preparing the input state, referred to as $\mathcal{A}$.
• grover_operator (Union[QuantumCircuit, CircuitFactory, None]) – The Grover operator $\mathcal{Q}$ used as unitary in the phase estimation circuit.
• objective_qubits (Optional[List[int]]) – A list of qubit indices. A measurement outcome is classified as ‘good’ state if all objective qubits are in state $|1\rangle$, otherwise it is classified as ‘bad’.
• post_processing (Optional[Callable[[float], float]]) – A mapping applied to the estimate of $0 \leq a \leq 1$, usually used to map the estimate to a target interval.
• 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
• initial_state (Optional[QuantumCircuit]) – A state to prepend to the constructed circuits.
• quantum_instance (Union[QuantumInstance, Backend, BaseBackend, None]) – Quantum Instance or Backend

Raises

AquaError – if the method to compute the confidence intervals is not supported

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) for more detail.

Returns

the A operator as CircuitFactory

Return type

CircuitFactory

Returns backend.

Return type

Union[Backend, BaseBackend]

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

QuantumCircuit

Returns

The circuit Q^k A |0>.

Get the $\mathcal{Q}$ operator, or Grover operator.

If the Grover operator is not set, we try to build it from the $\mathcal{A}$ operator and objective_qubits. This only works if objective_qubits is a list of integers.

Return type

Optional[QuantumCircuit]

Returns

The Grover operator, or None if neither the Grover operator nor the $\mathcal{A}$ operator is set.

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) 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

is_good_state(measurement)

Determine whether a given state is a good state.

Parameters

measurement (str) – A measurement as bitstring, e.g. ‘01100’.

Return type

bool

Returns

True if the measurement corresponds to a good state, False otherwise.

Raises

ValueError – If self.objective_qubits is not set.

Get the criterion for a measurement outcome to be in a ‘good’ state.

Return type

Optional[List[int]]

Returns

The criterion as list of qubit indices.

post_processing(value)

Post processing of the raw amplitude estimation output $0 \leq a \leq 1$.

Parameters

value (float) – The estimation value $a$.

Return type

float

Returns

The value after post processing, usually mapping the interval $[0, 1]$ to the target interval.

Returns the target precision epsilon of the algorithm.

Return type

float

Returns

The target precision (which is half the width of the confidence interval).

Get the Q operator, or Grover-operator for the Amplitude Estimation algorithm, i.e.

where $\mathcal{S}_0$ reflects about the |0>_n state and S_psi0 reflects about $|\Psi_0\rangle_n$. See https://arxiv.org/abs/quant-ph/0005055 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

Returns quantum instance.

Return type

Optional[QuantumInstance]

Return a numpy random.

run(quantum_instance=None, **kwargs)

Execute the algorithm with selected backend.

Parameters

• quantum_instance (Union[QuantumInstance, Backend, 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(backend, **kwargs)

Sets backend with configuration.

Return type

None

Get the $\mathcal{A}$ operator encoding the amplitude $a$.

Return type

QuantumCircuit

Returns

The $\mathcal{A}$ operator as QuantumCircuit.