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arXiv · 2406.06803

Leveraging modular values in quantum algorithms: the Deutsch-Jozsa

Lorena Ballesteros Ferraz·Timoteo Carletti·Yves Caudano
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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.

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Lorena Ballesteros Ferraz, Timoteo Carletti, Yves Caudano. 2024-06-10. Leveraging modular values in quantum algorithms: the Deutsch-Jozsa. https://arxiv.org/abs/2406.06803

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