**Mauro Mezzini**

Mauro Mezzini has been an Assistant Professor of Computer Science at the Roma Tre University since 2012. Previously, he was Adjunct Professor at La Sapienza University (2005–2011) and Project Manager at Telecom Italia (1990–2012). Some of his works have been published in SIAM Journals on computing, aCm transaction on information and system security, discrete applied mathematics and theoretical computer science. He has been a Guest Editor for the Special Issues "Quantum Computing Algorithms and Computational Complexity" and "Quantum Computing Algorithms and Quantum Computing Simulators", both belonging to the Mathematics and Computer Science sections of the Mathematics journal. His research interests include quantum computing, machine learning, graph theory and algorithm, databases and discrete mathematics.

## *Editorial* **Preface to the Special Issue on "Quantum Computing Algorithms and Computational Complexity"**

**Fernando L. Pelayo 1,\*and Mauro Mezzini 2,\***


#### **1. Call for Papers**

In 1982, Richard Feynman stated that in order to simulate quantum systems, we would rather go for a sort of brand-new powered quantum processor instead of a classical one. Since then, Quantum Computation has been growing in terms of both architectural issues associated with such quantum computers and the algorithms that can be run with them. All this has attracted much interest from the computer science community.

Just to mention some facts, it is obvious that the intrinsic parallelism that comes with the superposition of quantum states together with interference features provides us with a very good perspective to deal with heavy computational problems, such as encrypting/decrypting tasks or studying quantum issues of matter.

Quantum computing is a hot field of research at the intersection of mathematics, computer science, and physics that promises to significantly revolutionise many aspects of the technology industry such as medicine, machine learning, artificial intelligence, cryptography, and operations research to name a few. Investors and governments from all over the world promote its development considering that it is crucial and of strategic importance for countries, companies and, therefore, society as a whole. The huge investments in resources to develop quantum computing by countries such as China, India, the United States, Russia, and so on only confirms this reality.

This Special Issue was mainly concerned with quantum algorithms, the mathematics underlying them, and those complexity issues arising from them.

## **2. Published Papers**

This is a Special Issue of *Mathematics* belonging to the section "Mathematics and Computer Science", which was closed on 30 June 2022.

A total of 13 papers were submitted to it, of which 7 have been accepted. This represents an acceptance ratio of 53.8%. The average time for accepted papers to be published is 43.4 days.

The main contributions of these seven papers are the following:

Two of these seven papers are focused on improving the performance by means of quantum algorithms over the best instances of classical ones:


**Citation:** Pelayo, F.L.; Mezzini, M. Preface to the Special Issue on "Quantum Computing Algorithms and Computational Complexity". *Mathematics* **2022**, *10*, 4032. https://doi.org/10.3390/ math10214032

Received: 19 October 2022 Accepted: 21 October 2022 Published: 30 October 2022

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k", "the most frequent string search problem", and "searching intersection of two sequences of strings". Based on the quantum procedure for comparing two strings of length *k* in *O*( √*k*) queries, they are able to reduce time complexities, thus moving the factor *k* to √*k* in all its instances as parameters.

Another four papers deal with former quantum algorithms (or part of them) for which some improvements or different perspectives have been addressed:


Finally, there is a paper that researches a classical Operational Research problem by means of quantum annealing:

• Saul Gonzalez-Bermejo, Guillermo Alonso-Linaje, and Parfait Atchade-Adelomou, in their paper "GPS: A New TSP Formulation for Its Generalizations Type QUBO" [7], propose a new Quadratic Unconstrained Binary Optimization (QUBO) formulation of the Travelling Salesman Problem (TSP) with a smaller number of necessary variables, together with a thorough study of the constraints and their management. This study includes a practical test over D-wave quantum annealers platform.

As Guest Editors of this Special Issue, we would like to thank all the authors who make contributions on these quite conceptually similar fields of research.

We also would like to thank all the reviewers for their big effort in developing so constructive reports that contribute to improve the quality and quantity of the results provided within this Special Issue on "Quantum Computing Algorithms and Computational Complexity".

We hope that the research papers published in this Special Issue promote more extensive research and lend further support to quantum computing. We are believers of the wide and crucial effect that quantum computing can have in our society, from the domain of energy-efficient computing, through to high-performance computing, up to the managemen<sup>t</sup> of many of the most challenging problems which still remain open.

**Author Contributions:** All authors have contributed equally. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
