Abstract
After Google reported its realization of quantum supremacy, Solving the classical problems with quantum computing is becoming a valuable research topic. Switching function minimization is an important problem in Electronic Design Automation (EDA) and logic synthesis, most of the solutions are based on heuristic algorithms with a classical computer, it is a good practice to solve this problem with a quantum processer. In this paper, we introduce a new hybrid classic quantum algorithm using Grover’s algorithm and symmetric functions to minimize small Disjoint Sum of Product (DSOP) and Sum of Product (SOP) for Boolean switching functions. Our method is based on graph partitions for arbitrary graphs to regular graphs, which can be solved by a Grover-based quantum searching algorithm we proposed. The Oracle for this quantum algorithm is built from Boolean symmetric functions and implemented with Lattice diagrams. It is shown analytically and verified by simulations on a quantum simulator that our methods can find all solutions to these problems.
Highlights
Grover’s Algorithm [1] is one of few most famous and most useful quantum algorithms to which many decision and optimization problems can be reduced
The Boolean symmetric functions, Lattice diagrams are presented, the quantum layout of Lattice diagrams is shown in the end, this is the core part of symmetric blocks in our oracle
Please note that our hybrid algorithm calls Grover’s algorithm several times with new oracles created on the base of partial results returned from the previous runs of the quantum computer. We found that this principle is applicable to several other problems of logic synthesis in which the existing classical algorithm is converted to a hybrid algorithm based on Grover, in which the quantum algorithm is used only as a subroutine to execute search problems
Summary
Grover’s Algorithm [1] is one of few most famous and most useful quantum algorithms to which many decision and optimization problems can be reduced. We present a uniform approach to use Grover’s Algorithm for solving several problems in Graph Theory which has multiple applications such as minimization of binary circuits [2]. A DSOP realization of a Boolean function can be represented as a hypercube graph in which a realization with disjoint products of literals corresponds to disjoint partitioning to sub-hypercubes. The classical part of the algorithm is executed on the classical computer which prepares data and controls for the quantum computer and receives partial results from it With such a hybrid algorithm, we are able to distinguish special cases of E-regular graphs such as cycles, standard hypercubes and some generalized hypercubes. The main innovative idea of our paper is to represent Graph Theory problems as collections of symmetric functions in which variables correspond to edges of the graph and nodes to certain constraints on them.
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