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arXiv:1510.03365 · Physics Letters A

Quantum computation with classical light: The Deutsch Algorithm

Benjamin Perez-García, Jason Francis, Melanie G. McLaren, Raúl I. Hernández-Aranda, Andrew Forbes, Thomas Konrad

Published Apr 25, 2015• 58 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2015.04.034

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Deutsch's problem is the simplest and most frequently examined example of computational problem used to demonstrate the superiority of quantum computing over classical computing. Deutsch's quantum algorithm has been claimed to be faster than any classical ones solving the same problem, only to be discovered later that this was not the case. Various de-quantised solutions for Deutsch's quantum algorithm—classical solutions which are as efficient as the quantum one—have been proposed in the literature. These solutions are based on the possibility of classically simulating "superpositions", a key ingredient of quantum algorithms, in particular, Deutsch's algorithm. The de-quantisation proposed in this note is based on a classical simulation of the quantum measurement achieved with a model of observed system. As in some previous de-quantisations of Deutsch's quantum algorithm, the resulting de-quantised algorithm is deterministic. Finally, we classify observers (as finite state automata) that can solve the problem in terms of their "observational power".
Abstract: Over the last decade has been a lot of interest in new types of computable machines, due partly over the fears on conventional, classical, computing. Research by leading physicists, mathematicians and computer scientists has shown quantum computers could be the future, as they may be able to solve some computationally difficult problems much faster than is currently possible on a classical computer. David Deutsch has already created a working model for a quantum computer, the quantum Turing machine or QTM Deutsch [1985]. This has been proved as a model for computation on a quantum and has allowed algorithms to be developed. Deutsch-Josza’s algorithm, as all known quantum algorithms that provide exponential speedup over classical systems do, answers a question about a global property of a solution space. This paper describes the generalization of the Deutsch-Josza algorithm to n d-dimensional quantum systems or qudits. Key–Words: quantum computing, quantum dits, quantum algorithm 1
The well-known Deutsch Algorithm (DA) and Deutsch-Jozsha Algorithm (DJA) both are used as an evidence to the power of quantum computers over classical computation mediums. In these theoretical experiments, it has been shown that a quantum computer can find the answer with certainty within a few steps although classical electronic systems must evaluate more iterations than quantum computer. In this paper, it is shown that a classical computation system formed by using ordinary electronic parts may perform the same task with equal performance than quantum computers. DA and DJA quantum circuits act like an analog computer, so it is unfair to compare the bit of classical digital computers with the qubit of quantum computers. An analog signal carrying wire will of course carry more information that a bit carrying wire without serial communication protocols.