Linear optical demonstration of quantum speed-up with a single qudit

TL;DR

This paper demonstrates a quantum speed-up using a single four-level quantum system (qudit) with linear optics, showing that even a single qudit can outperform classical algorithms in specific oracle-based problems.

Contribution

It experimentally proves that a single qudit can achieve quantum speed-up, extending the understanding of quantum advantage with minimal quantum resources.

Findings

Single qudit suffices for quantum speed-up in an oracle problem

Experimental realization with linear optical elements

Speed-up ratio of two-to-one demonstrated

Abstract

Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding quantum physics, the origin of the power of quantum algorithm is still an open question. Non-classical correlation is regarded as the most possible answer for the open question. However we experimentally realize a quantum speed-up algorithm on four-level system with linear optical elements and prove that even a single qudit is enough for designing an oracle-based algorithm which can solve a model problem twice faster than any classical algorithm. The algorithm can be generalized to higher dimensional qudits with the same two-to-one speed-up ratio.