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International Russian Automation Conference (RusAutoCon)

Model Design of Quantum Logic Circuits Based on Reed-Muller Expressions

Irina Matveeva, В. А. Калмычков, Anatolii Dorokhov

Published Sep 1, 2018• 2 citations
Publisher

Abstract

The article considers the design flow for automatic generation of the quantum circuit model specifications as a fragment of the logical unit of a quantum computer. Reed-Muller expressions is base for this generation. The model representation takes into account the features of the quantum circuit realization in the notation of the linear nearest neighborhood (LNN), the proposed templates provide the automatic selection of the optimal gates composition.

DOI
10.1109/rusautocon.2018.8501822

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The article considers the design flow for automatic generation of the quantum circuit model specifications as a fragment of the logical unit of a quantum computer. Reed-Muller expressions is base for this generation. The model representation takes into account the features of the quantum circuit realization in the notation of the linear nearest neighborhood (LNN), the proposed templates provide the automatic selection of the optimal gates composition.
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Combining several kinds of ideas of synthesis of reversible logic circuits,this paper presents a novel and efficient algorithm which can automatically derive the positive polarity Reed-Muller expansion(RM).A solution space tree of creating quantum reversible logic circuits is constructed.Firstly floor traversal is used in whole,and depth-first search is used in local.Secondly according to the technique of template optimization,the bound function is created which can rapidly eliminate the branches of none result or none optimal result.Thirdly factors of RM are considered first.Therefore the algorithm can effectively construct optimal result and saves computational cost significantly.
Abstract—Quantum Boolean circuit synthesis issues are becoming a key area of research in the domain of quantum computing. For gate-level synthesis, minterm based and Reed-Muller canonical decomposition techniques are adopted as common approaches. Physical implementation of quantum circuits have inherent constraints and hence nearest neighbour template of input lines is gaining importance. In this work, we present a brief analysis of the various Fixed Polarity Reed Muller (FPRM) expressions for a given quantum Boolean circuit and also introduce the rules for the nearest neighbour template-based synthesis of these forms. The corresponding circuit costs are evaluated.
The article describes the method of design of quantum circuit specifications, based on tabulated Boolean functions data. The method is considered as an example of building a set of new Boolean quantum circuits synthesized based on Reed – Muller polarized polynomials (FPRM) to have the best polynomial forms on the basis of preliminary statistical analysis of certain FPRM characteristics at all polarities. Matrix entry and software implementation of basic quantum converters is described, includind: NOT, C1NOT, C2NOT, SWAP. An example of the construction of a set of quantum circuits for quantum Boolean function for a given 1–0 table presented. The article shows, that the problem of synthesis and optimization of quantum circuits can be reduced to the traditional logical decisions. Illustrations, demonstrating transitions from automatically synthesized quantum circuits for different polarities of the Reed-Muller polynomials to quantum circuits with the least number of converters, presented.