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Journal of Physics Conference Series

Enhancing the quantum cost of Reed-Muller Based Boolean quantum circuits using genetic algorithms

Mohamed Samir Shaban, Ahmed Younes, Ashraf Elsayed

Published Jan 1, 2020• 1 citation
Publisher

Abstract

Abstract There is a direct equivalence between Boolean functions represented in Reed-Muller logic and Boolean Quantum Circuits. Different polarity Reed-Muller expansions will give different Boolean quantum circuits with different cost for the same Boolean function. For a given Boolean function with n variables there are 2n possible expansions. Searching for the expansion that gives a Boolean quantum circuit with minimum quantum cost within the search space is a hard problem for large n. This paper will use genetic algorithms to find the fixed/mixed polarity Reed-Muller expansion that gives a Boolean quantum circuit with minimum quantum cost to optimize the circuit realization of a given Boolean function.

DOI
10.1088/1742-6596/1447/1/012031

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Abstract There is a direct equivalence between Boolean functions represented in Reed-Muller logic and Boolean Quantum Circuits. Different polarity Reed-Muller expansions will give different Boolean quantum circuits with different cost for the same Boolean function. For a given Boolean function with n variables there are 2n possible expansions. Searching for the expansion that gives a Boolean quantum circuit with minimum quantum cost within the search space is a hard problem for large n. This paper will use genetic algorithms to find the fixed/mixed polarity Reed-Muller expansion that gives a Boolean quantum circuit with minimum quantum cost to optimize the circuit realization of a given Boolean function.
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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.
It has been experimentally proven that realizing universal quantum gates using higher-radices logic is practically and technologically possible. We developed a Parallel Genetic Algorithm that synthesizes Boolean reversible circuits realized with a variety of quantum gates on qudits with various radices. In order to allow synthesizing circuits of medium sizes in the higher radix quantum space we performed the experiments using a GPU accelerated Genetic Algorithm. Using the accelerated GA we compare heuristic improvements to the mutation process based on cost minimization, on the adaptive cost of the primitives and improvements due to Baldwinian vs. Lamarckian GA. We also describe various fitness function formulations that allowed for various realizations of well known universal Boolean reversible or quantum-probabilistic circuits.