Quantum computation speedup limits from quantum metrological precision bounds

TL;DR

This paper establishes a connection between quantum metrological precision bounds and the query complexity of quantum search algorithms, revealing how decoherence impacts quantum speed-up.

Contribution

It introduces a scheme translating metrological bounds into lower bounds on quantum search query complexity, linking quantum metrology and quantum computing performance.

Findings

Quadratic quantum speed-up is lost under decoherence.

Metrological precision bounds can inform quantum algorithm complexity.

The approach reveals fundamental limits on quantum computational advantage.

Abstract

We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and quantum computing schemes becomes clear. More importantly, we utilize results from the field of quantum metrology on a generic loss of quadratic quantum precision enhancement in presence of decoherence to infer an analogous generic loss of quadratic speed-up in oracle based quantum computing. While most of our reasoning is rigorous, at one of the final steps, we need to make use of an unproven technical conjecture. We hope that we will be able to amend this deficiency in the near future, but we are convinced that even without the conjecture proven our results provide a novel and deep insight into relationship between quantum algorithms and quantum metrology protocols.