Evolutionary Quantum Logic Synthesis of Boolean Reversible Logic Circuits Embedded in Ternary Quantum Space using Heuristics (original) (raw)
Related papers
IEEE Congress on Evolutionary Computation, 2010
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.
Application of Genetic Algorithms for Evolution of Quantum Equivalents of Boolean Circuits
Due to the non-intuitive nature of Quantum algorithms, it becomes difficult for a classically trained person to efficiently construct new ones. So rather than designing new algorithms manually, lately, Genetic algorithms (GA) are being implemented for this purpose. GA is a technique to automatically solve a problem using principles of Darwinian evolution. This has been implemented in this paper to explore the possibility of evolving an n-qubit circuit when the circuit matrix has been provided using a set of single, two and three qubit gates. Using a variable length population and universal stochastic selection procedure, a number of possible solution circuits, with different number of gates can be obtained for the same input matrix during different runs of GA. The given algorithm has also been successfully implemented to obtain two and three qubit Boolean circuits using Quantum gates. The results demonstrate the relative effectiveness of the GA procedure in providing better solutions in a reasonable computation time even when the search spaces are large.
Evolutionary Approach to Quantum and Reversible Circuits Synthesis
Artificial Intelligence in Logic Design, 2004
The paper discusses the evolutionary computation approach to the problem of optimal synthesis of Quantum and Reversible Logic circuits. Our approach uses standard Genetic Algorithm (GA) and its relative power as compared to previous approaches comes from the encoding and the formulation of the cost and fitness functions for quantum circuits synthesis. We analyze new operators and their role in synthesis and optimization processes. Cost and fitness functions for Reversible Circuit synthesis are introduced as well as local optimizing transformations. It is also shown that our approach can be used alternatively for synthesis of either reversible or quantum circuits without a major change in the algorithm. Results are illustrated on synthesized Margolus, Toffoli, Fredkin and other gates and Entanglement Circuits. This is for the first time that several variants of these gates have been automatically synthesized from quantum primitives.
Enhanced Quantum Inspired Evolutionary Algorithm For Automatic Synthesis of Reversible Circuits
2016
Reversible Logic Synthesis is an important area of current research because there is theoretical basis that shows that reversible circuits can be constructed for computing without any loss of information and, therefore, without expending energy. However, design of these circuits is a difficult problem as there is no standard algorithmic approach available. Quantum Inspired Evolutionary Algorithms (QIEA) combine ideas from Quantum Computing and Evolutionary Algorithms for effective search and optimization. They rely on the immense representation power offered by Quantum Bits and search using Quantum operators. These have been shown to be effective on a wide variety of problems. This paper introduces a novel QIEA called the Enhanced Quantum Inspired Evolutionary Algorithm (EQIEA) for the automatic synthesis of reversible classical circuits like Binary to Gray converters, Gray to Binary Converters, Boolean functions and Arithmetic Circuits. It has been shown that EQIEA not only takes m...
Genetic Algorithm based synthesis of ternary Reversible/Quantum circuit
Reversible / Quantum circuits are believed to be one of the future computer technologies. In this paper, a Genetic Algorithm (GA) based synthesis of ternary reversible / quantum circuits using Muthukrishnan-Stroud gates is presented. The circuit generated by GA may contain redundant gates. We have used post GA reduction to eliminate these redundant gates. We have experimented with ternary half-adder circuit. The proposed GA converges for many combinations of crossover and mutation.. Index Terms — Reversible logic, half-adder, quantum circuit, post GA reduction..
This paper illustrates the application of a Hybrid Quantum Inspired Evolutionary Algorithm (HQIEA) in evolving a variety of Quantum equivalents of classical circuits. Taking the matrix corresponding to an oracle as input, this HIQEA designs classical circuits using quantum gates. A library consisting of single, two and three qubit Quantum gates and the desired circuit matrix were given as input and algorithm was able to successfully design half adder, full adder and binary-gray conversion circuits apart from circuits for two, three and four qubit Boolean functions, using Quantum gates. The circuits obtained compare favorably with earlier attempts in terms of number of gates, ancillary inputs and garbage outputs required for constructing these circuits and the time taken to evolve them.
Quantum encoded quantum evolutionary algorithm for the design of quantum circuits
2019
In this paper we present Quanrum Encoded Quantum Evolutionary Algorithm (QEQEA) and compare its performance against a a classical GPU accelerated Genetic Algorithm (GPUGA). The proposed QEQEA differs from existing quantum evolutionary algorithms in several points: representation of candidates circuits is using qubits and qutrits and the proposed evolutionary operators can theoretically be implemented on quantum computer provided a classical control exists. The synthesized circuits are obtained by a set of measurements performed on the encoding units of quantum representation. Both algorithms are accelerated using (general purpose graphic processing unit) GPGPU. The main target of this paper is not to propose a completely novel quantum genetic algorithm but to rather experimentally estimate the advantages of certain components of genetic algorithm being encoded and implemented in a quantum compatible manner. The algorithms are compared and evaluated on several reversible and quantum ...
Enhancing the quantum cost of Reed-Muller Based Boolean quantum circuits using genetic algorithms
Journal of Physics: Conference Series, 2020
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.
We present a comparative study in the Evolutionary Quantum Logic Synthesis (EQLS) of Quantum Circuits (QC). The objective of this paper focuses on the high speed Evolutionary Algorithms for the synthesis of Quantum circuits. In particular, we describe the comparison between an efficient representation of the synthesized quantum circuit as Quantum Multi-valued Decision Diagram (QMDD) and a low level parallelized evaluation method using the hardware accelerated matrix manipulation. As it is shown in the experiments, each approach has its limits and advantages, and an appropriate choice of each of them yield better results for a subset of the QLS.
Synthesis of Quantum Circuits Using Genetic Algorithm
2009
The need of efficient technique for synthesis of quantum circuits is of immense importance in defining efficient hardware for quantum computers. In this work, a new automated approach for quantum circuit synthesis using genetic algorithm has been presented. The methodology of building a quantum circuit corresponding to a given quantum operation, expressed in terms of a unitary transform matrix, utilizing a specified quantum gate library has been proposed in this paper. Experimental results show that this technique using GA is better than other methods used for this purpose.