qrisp.quantum_backtracking.QuantumBacktrackingTree.estimate_phase#

QuantumBacktrackingTree.estimate_phase(precision)[source]#

Performs quantum phase estimation on the quantum step operator.

If executed with sufficient precision, the phase estimation will yield a QuantumFloat, where the probability of the 0 component indicates the presence of a node where the accept function yielded True.

If the probability is higher than 3/8 $\Rightarrow$ A solution exists.

If the probability is less than 1/4 $\Rightarrow$ No solution exists.

Otherwise $\Rightarrow$ Increase precision.

In general, the required precision is proportional to

$$\frac{{\text{log}}_2(Tn)}{2}+\beta$$

Where $T$ is the amount of nodes, that would be visited by a classical algorithm, $n$ is the maximum depth and $\beta$ is a universal constant.

Parameters:

precisionint

The precision to perform the quantum phase estimation with.

Returns:

qpe_resQuantumFloat

The QuantumFloat containing the result of the phase estimation.