Leveraging modular values in quantum algorithms: the Deutsch-Jozsa

TL;DR

This paper introduces a new quantum algorithm leveraging modular values to enhance the Deutsch-Jozsa problem, offering more optimization flexibility and potential for future improvements in quantum computing.

Contribution

It presents the first application of modular values in quantum algorithms, specifically modifying the Deutsch-Jozsa algorithm for better optimization options.

Findings

Prototype tested on quantum platform with promising insights.

Current results are below conventional methods but indicate future potential.

Exploration of pre- and post-selected states enhances algorithm flexibility.

Abstract

We present a novel approach to quantum algorithms, by taking advantage of modular values, i.e., complex and unbounded quantities resulting from specific post-selected measurement scenarios. Our focus is on the problem of ascertaining whether a given function acting on a set of binary values is constant (uniformly yielding outputs of either all 0 or all 1), or balanced (a situation wherein half of the outputs are 0 and the other half are 1). Such problem can be solved by relying on the Deutsch-Jozsa algorithm. The proposed method, relying on the use of modular values, provides a high number of degrees of freedom for optimizing the new algorithm inspired from the Deutsch-Jozsa one. In particular, we explore meticulously the choices of the pre- and post-selected states. We eventually test the novel theoretical algorithm on a quantum computing platform. While the outcomes are currently not on par with the conventional approach, they nevertheless shed light on potential for future improvements, especially with less-optimized algorithms. We are thus confidend that the proposed proof of concept could prove its validity in bridging quantum algorithms and modular values research fields.