Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Conference on Electrical and Computer Engineering (ICECE)

A Quantum Logic Circuit For Generating Fixed-Polarity Reed-Muller Coefficients

Mozammel H. A. Khan

Published Dec 1, 2006• 0 citations
Publisher

Abstract

Logic function representation using fixed-polarity Reed-Muller (FPRM) expression has manifold advantages over classical SOP expression. Moreover, FPRM expression is a very useful representation for logic function realization using quantum logic circuits. In this paper, we present a quantum logic circuit for generating FPRM coefficients for a given polarity vector from the truth vector of the function

DOI
10.1109/icece.2006.355310

Related papers

A Quantum CAD Accelerator Based on Grover’s Algorithm for Finding the Minimum Fixed Polarity Reed-Muller Form

Lun Li, Mitchell Aaron Thornton, Marek A. Perkowski

We describe the use of Grover’s algorithm as implemented in a quantum logic circuit that produces a solution for a classical switching circuit design problem. The particular application described here is to determine a Fixed Polarity Reed-Muller (FPRM) form that satisfies a threshold value constraint, thus we find a particular FPRM form among all 2^n FPRM forms that has a number of terms less than or equal to the threshold value. Grover’s algorithm is implemented in a quantum logic circuit that also contains a subcircuit that expresses all possible FPRM solutions of a given function. This approach illustrates how fast transforms as known from spectral theory can be combined with quantum computing as a part of an oracle.

IEEE International Symposium on Multiple-Valued Logic (ISMVL)•Jan 1, 2006•9 citations

Nearest Neighbour based Synthesis of Quantum Boolean Circuits

Amlan Chakrabarti, Susmita Sur‐Kolay

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.

Engineering letters•Jan 1, 2007•29 citations

Проектирование спецификаций квантовой цепи на основе анализа статистической информации

Irina Matveeva, К. В. Власова, М. А. Линник +2 more

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.

Современные проблемы науки и образования•Jan 1, 2013•0 citations

Representation of Boolean Quantum Circuits as Reed-Muller Expansions

Ahmed Younes, Julian Francis Miller

In this paper we show that there is a direct correspondence between quantum Boolean operations and certain forms of classical (non-quantum) logic known as Reed-Muller expansions. This allows us to readily convert Boolean circuits into their quantum equivalents. A direct result of this is that the problem of synthesis and optimization of quantum Boolean logic can be tackled within the field of Reed-Muller logic.

arXiv:quant-ph/0305134•May 22, 2003•0 citations

Representation of Boolean quantum circuits as reed–Muller expansions

Ahmed Younes, Julian F. Miller

In this paper we show that there is a direct correspondence between Boolean quantum operations and certain forms of classical (non-quantum) logic known as Reed–Muller expansions. This allows us to readily convert Boolean circuits into their quantum equivalents. A direct result of this is that the problem of synthesis and optimization of Boolean quantum circuits can be tackled within the field of Reed–Muller logic.

International Journal of Electronics•Jul 1, 2004•37 citations

Minimization of AND-XOR Expressions with Decoders for Quantum Circuits

Sonia Yang, Ali Al-Bayaty, Marek Perkowski

This paper introduces a new logic structure for reversible quantum circuit synthesis. Our synthesis method aims to minimize the quantum cost of reversible quantum circuits with decoders. In this method, multi-valued input, binary output (MVI) functions are utilized as a mathematical concept only, but the circuits are binary. We introduce the new concept of ``Multi-Valued Input Fixed Polarity Reed-Muller (MVI-RM)" forms. Our decoder-based circuit uses three logical levels in contrast to commonly-used methods based on Exclusive-or Sum of Products (ESOP) with two levels (AND-XOR expressions), realized by Toffoli gates. In general, the high number of input qubits in the resulting Toffoli gates is a problem that greatly impacts the quantum cost. Using decoders decreases the number of input qubits in these Toffoli gates. We present two practical algorithms for three-level circuit synthesis by finding the MVI-FPRM: products-matching and the newly developed butterfly diagrams. The best MVI-FPRM forms are factorized and reduced to approximate Multi-Valued Input Generalized Reed-Muller (MVI-GRM) forms.

quant-pharXiv:2601.02515•Jan 7, 2026•0 citations
Logic function representation using fixed-polarity Reed-Muller (FPRM) expression has manifold advantages over classical SOP expression. Moreover, FPRM expression is a very useful representation for logic function realization using quantum logic circuits. In this paper, we present a quantum logic circuit for generating FPRM coefficients for a given polarity vector from the truth vector of the function
We describe the use of Grover’s algorithm as implemented in a quantum logic circuit that produces a solution for a classical switching circuit design problem. The particular application described here is to determine a Fixed Polarity Reed-Muller (FPRM) form that satisfies a threshold value constraint, thus we find a particular FPRM form among all 2^n FPRM forms that has a number of terms less than or equal to the threshold value. Grover’s algorithm is implemented in a quantum logic circuit that also contains a subcircuit that expresses all possible FPRM solutions of a given function. This approach illustrates how fast transforms as known from spectral theory can be combined with quantum computing as a part of an oracle.
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.
This paper introduces a new logic structure for reversible quantum circuit synthesis. Our synthesis method aims to minimize the quantum cost of reversible quantum circuits with decoders. In this method, multi-valued input, binary output (MVI) functions are utilized as a mathematical concept only, but the circuits are binary. We introduce the new concept of ``Multi-Valued Input Fixed Polarity Reed-Muller (MVI-RM)" forms. Our decoder-based circuit uses three logical levels in contrast to commonly-used methods based on Exclusive-or Sum of Products (ESOP) with two levels (AND-XOR expressions), realized by Toffoli gates. In general, the high number of input qubits in the resulting Toffoli gates is a problem that greatly impacts the quantum cost. Using decoders decreases the number of input qubits in these Toffoli gates. We present two practical algorithms for three-level circuit synthesis by finding the MVI-FPRM: products-matching and the newly developed butterfly diagrams. The best MVI-FPRM forms are factorized and reduced to approximate Multi-Valued Input Generalized Reed-Muller (MVI-GRM) forms.