qrisp.quantum_backtracking.QuantumBacktrackingTree.estimate_phase

QuantumBacktrackingTree.estimate_phase(precision)

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.