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Revista Mexicana de Física E

Algoritmo cuántico de Deutsch y Jozsa en GAMA

Mireya Paredes, A. Meneses Viveros, Guillermo B. Morales-Luna

Published Jun 11, 2018• 2 citations
Publisher

Abstract

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.

DOI
10.31349/revmexfise.64.181

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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.
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.
Quantum computing takes fully advantage of the superposition principle to increase greatly (even exponentially) the speed of calculations, relative to the classical approach. The Deutsch-Jozsa algorithm is the simplest quantum algorithm illustrating this power. Unfortunately, the standard derivation involves several ingenious steps which usually leave students feeling that they could never have figured out the algorithm by themselves. We present here a different formulation of the problem which allows students to derive the algorithm using only basic knowledge of quantum mechanics and linear algebra.
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