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Revista Tecnológica da Fatec Americana

Comparação de desempenho do algoritmo de Deutsch-Jozsa nas linguagens quânticas Silq e Qasm

Mariana Godoy Vazquez Miano, Lucas Gomes Pinheiro, Sthefanie Costa Amaro, Victor Luis Rodrigues Pereira Ferreira

Published Nov 6, 2023• 0 citations
Publisher

Abstract

Due to the importance given to information in the last few decades, a performance and processing advantage of information becomes relevant, something that can be found through quantum computing. The Deutsch-Jozsa Algorithm is the first example of a quantum algorithm that offers an exponential advantage against classical algorithms, whether in a local environment or through cloud simulators. Seeking to explore the advantages of quantum computation, the Deutsch-Jozsa Algorithm was implemented in two quantum programming languages, namely the high level language Silq, focused on the execution of the algorithm on a local environment through VSCode, which offers a cleaner and friendly sintaxe as well as quantum uncomputation, and also in OpenQASM, a low level language meant to interact with quantum circuits, used to better visualize the Deutsch-Jozsa Algorithm. This paper aims to make the differences between high and low-level quantum languages clear, as well as incentivize the change to a new paradigm.

DOI
10.47283/244670492023110147

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Due to the importance given to information in the last few decades, a performance and processing advantage of information becomes relevant, something that can be found through quantum computing. The Deutsch-Jozsa Algorithm is the first example of a quantum algorithm that offers an exponential advantage against classical algorithms, whether in a local environment or through cloud simulators. Seeking to explore the advantages of quantum computation, the Deutsch-Jozsa Algorithm was implemented in two quantum programming languages, namely the high level language Silq, focused on the execution of the algorithm on a local environment through VSCode, which offers a cleaner and friendly sintaxe as well as quantum uncomputation, and also in OpenQASM, a low level language meant to interact with quantum circuits, used to better visualize the Deutsch-Jozsa Algorithm. This paper aims to make the differences between high and low-level quantum languages clear, as well as incentivize the change to a new paradigm.
An important feature of quantum computing is its inherent paralellism, allowing to process an exponential number of basic transforms with just a linear number of qubits. The Deutsch-Jozsa algorithm exemplifies the computational complexity reduction. This work reports the implementation and execution of the Deutsch-Josza quantum algoritm in GAMA, a programming language for quantum computing simulation developed by ourselves. Through this simulation, it is possible to explore all the components involved by tracing all the different configurations that each component may take.
Quantum computing, with its vast potential, is fundamentally shaped by the intricacies of quantum mechanics, which both empower and constrain its capabilities. The development of a universal, robust quantum programming language has emerged as a key research focus in this rapidly evolving field. This paper explores Silq, a recent high-level quantum programming language, highlighting its strengths and unique features. We aim to share our insights on designing and implementing high-level quantum algorithms using Silq, demonstrating its practical applications and advantages for quantum programming.
Abstract In the field of quantum computing, the Deutsch–Jozsa problem serves as a classical example illustrating the computational advantages of quantum algorithms over classical counterparts in specific scenarios. The problem involves efficiently determining the nature of a multi-valued function, showcasing how quantum parallelism can accelerate problem-solving. The Deutsch–Jozsa algorithm provides a framework for exploring these quantum advantages and offers insights into optimization tasks such as the minimum spanning tree (MST) problem in network design. Applications include network engineering, routing optimization, and resource allocation, where quantum-enhanced approaches can potentially outperform classical methods. This study examines the implementation of the Deutsch–Jozsa algorithm on quantum simulators and its adaptation in quantum versions of classical MST algorithms, such as the Ambainis–Spalek quantum variant of Edmonds–Karp. The analysis highlights the role of Grover’s search as a foundational component, integrating it with quantum MST techniques. Practical simulations using IBM Quantum platforms illustrate the algorithm’s potential for network optimization and broader information security applications.
The Deutsch and Deutsch-Jozsa algorithms are foundational in the study of quantum computing, providing early and elegant demonstrations of quantum speedup over classical computation. This paper offers a pedagogical exposition of both algorithms, beginning with the necessary background in quantum computation and culminating in detailed, step-by-step derivations of the algorithms, complete with mathematical formulations and circuit diagrams. Simulations using quantum gates are also discussed to enhance understanding. The aim is to make these seminal algorithms accessible to readers with a basic background in linear algebra and quantum mechanics.
What are the advantages quantum computing can provide when compared to classical computing? In this thesis, we aim to answer this question from different perspectives. To achieve this goal we divided this work into three parts. In Part I we start by studying the basic principles of quantum computing. Next, we introduce two quantum algorithms: the Deutsch-Jozsa and Grovers algorithms. The first algorithm has a lower query complexity and the second has a lower time complexity when compared with the best classical algorithm for the same problems. The final topic of this initial part is a detailed explanation and example of how to use Grovers algorithm to solve a Boolean formula in conjunctive normal form. In the second part, we focus on communication complexity problems. These problems are usually stated as follows: two spatially separated parties Alice and Bob receive an input from a referee. Their goal is to compute the value of a function that depends on both of their inputs with the least amount of communication between them. In Part II we will introduce protocols in which the transmission of quantum bits (qubits), instead of bits, can reduce the amount of communication necessary to solve these problems. We also study how Alice and Bob can use quantum entanglement to solve two communication complexity problems without communicating something that can not be done classically. In Part III we study nonlocal games inspired by standard graph theory parameters. A nonlocal game is usually defined as a game in which players that can share and do computations in an entangled state have some sort of advantage over classical players. We begin this final part by introducing the quantum chromatic number of a graph, which is the minimal number of colors necessary in a nonlocal game in which Alice and Bob can convince a referee with certainty that they have a proper coloring of the graph. We end this thesis by introducing other two quantum graph parameters, one related to graph homomorphism and the other to the independence number of a graph.