Adaptive quantum phase estimation can be better than non-adaptive

TL;DR

This paper demonstrates that for certain phase estimation problems with specific promises, adaptive quantum algorithms can outperform non-adaptive ones by nearly a factor of two in the number of unitary applications, challenging previous assumptions.

Contribution

The paper provides the first examples where adaptive quantum phase estimation surpasses non-adaptive methods under certain conditions, with proven advantage bounds.

Findings

Adaptive methods outperform non-adaptive in specific cases

Nearly double efficiency in unitary applications for adaptive algorithms

Upper bounds on adaptive advantage established

Abstract

Quantum phase estimation is one of the most important tools in quantum algorithms. It can be made non-adaptive (meaning all applications of the unitary $U_\phi$ happen simultaneously) without using more applications of $U_\phi$, albeit at the expense of using many more qubits. It is also known that there is no advantage for adaptive algorithms in the case where the phase that needs to be estimated is arbitrary or is uniformly random. Here we give examples of a special case of phase estimation, with a promise on the values that the unknown phase can take, where adaptive methods are provably better than non-adaptive methods by a factor of nearly 2 in the number of uses of $U_\phi$. We also prove some upper bounds on the maximum advantage that adaptive algorithms for phase estimation can achieve over non-adaptive ones.