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Современные проблемы науки и образования

Проектирование спецификаций квантовой цепи на основе анализа статистической информации

Irina Matveeva, К. В. Власова, М. А. Линник, Е. Д. Синявская, Л. А. Фокин

Published Jan 1, 2013• 0 citations

Abstract

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.

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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.

The article deals with the interrelated set of design flows for quantum circuit, providing an integrative view on the basic procedures of their specifications design. The proposed use of flexible design flows should provide an analysis of model representations of quantum circuits from different sides (levels of perception and technological maintenance), their integration into modern means of development and simulation of quantum computing. The results of our approach application are demonstrated. Multistage procedures for designing of quantum circuits specifications with necessary characteristics are considered by means of the example of fixed polarity Reed-Muller expressions synthesis. The results of templates using for minimization of SWAP gates groups are presented for the purpose of quantum circuits obtaining in the linearly nearest neighborhood architecture. The analysis of automatically generated specifications of quantum circuits is based on a set of criteria.

Abstract The construction of quantum computers is based on the synthesis of low-cost quantum circuits. The quantum circuit of any Boolean function expressed in a Positive Polarity Reed-Muller (PPRM) expansion can be synthesized using Multiple-Control Toffoli (MCT) gates. This paper proposes two algorithms to construct a quantum circuit for any Boolean function expressed in a PPRM expansion. The Boolean function can be expressed with various algebraic forms, so there are different quantum circuits can be synthesized for the Boolean function based on its algebraic form. The proposed algorithms aim to map the MCT gates into the NCV gates for any quantum circuit by generating a simple algebraic form for the Boolean function. The first algorithm generates a special algebraic form for any Boolean function by rearrangement of terms of the Boolean function according to a predefined degree of term d term , then synthesizes the corresponding quantum circuit. The second algorithm applies the decomposition methods to decompose MCT circuit into its elementary gates followed by applying a set of simplification rules to simplify and optimize the synthesized quantum circuit. The proposed algorithms achieve a reduction in the quantum cost of synthesized quantum circuits when compared with relevant work in the literature. The proposed algorithms synthesize quantum circuits that can applied on IBM quantum computer.

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.