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IEEE International Symposium on Multiple-Valued Logic (ISMVL)

Study of GPU Acceleration in Genetic Algorithms for Quantum Circuit Synthesis

Martin Lukáč, Georgiy Krylov

Published May 1, 2017• 4 citations
Publisher

Abstract

In this work we present a comparative study of several GPU accelerated elements of a Genetic Algorithm (GA) for the synthesis of quantum circuits on the level of Electro-Magnetic (EM) pulses. The novelty in our approach is in the implementation: a) a completely GPU accelerated quantum simulator, b) GPU accelerated genetic operators and fitness evaluation and finally c) a set of GPU implemented optimizations for GPU accelerated evolutionary search optimization for the synthesis of quantum circuits. The reason for using EM pulses model for synthesis is the observation that this model requires the largest amount of elementary rotations to implement quantumlogic gates and thus provides a good measure to evaluate the efficiency of the acceleration by the GPU processor. The reason to use a GA is the advantage of pseudo evolutionary search in very large problem space such as the one defined by the Ising model where the EM realized quantum circuits are evolved. As a result of the several GPU optimizations several new circuits implementations are presented and their cost is compared to thecurrently known Ising model implementations.

DOI
10.1109/ismvl.2017.24

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In this work we present a comparative study of several GPU accelerated elements of a Genetic Algorithm (GA) for the synthesis of quantum circuits on the level of Electro-Magnetic (EM) pulses. The novelty in our approach is in the implementation: a) a completely GPU accelerated quantum simulator, b) GPU accelerated genetic operators and fitness evaluation and finally c) a set of GPU implemented optimizations for GPU accelerated evolutionary search optimization for the synthesis of quantum circuits. The reason for using EM pulses model for synthesis is the observation that this model requires the largest amount of elementary rotations to implement quantumlogic gates and thus provides a good measure to evaluate the efficiency of the acceleration by the GPU processor. The reason to use a GA is the advantage of pseudo evolutionary search in very large problem space such as the one defined by the Ising model where the EM realized quantum circuits are evolved. As a result of the several GPU optimizations several new circuits implementations are presented and their cost is compared to thecurrently known Ising model implementations.
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 circuits. The results demonstrate that on one hand the quantum encoding and quantum implementation compatible implementation provides certain disadvantages with respect to the classical evolutionary computation. On the other hand, encoding certain components in a quantum compatible manner could in theory allow to accelerate the search by providing small overhead when built in quantum computer. Therefore acceleration would in turn counter weight the implementation limitations.
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 in theory 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 in 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 circuits. The results demonstrate that on one hand the quantum encoding and quantum implementation compatible implementation provides certain disadvantages with respect to the classical evolutionary computation. On the other hand, encoding certain components in a quantum compatible manner could in theory allow to accelerate the search. This acceleration would in turn counter weight the implementation limitations.
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.
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.
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 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 effectiveness of the GA procedure even when the search spaces are large.
Designing efficient quantum circuits that leverage quantum advantage compared to classical computing has become increasingly critical. Genetic algorithms have shown potential in generating such circuits through artificial evolution. However, integrating quantum advantage into the fitness function of these algorithms remains unexplored. In this paper, we aim to enhance the efficiency of quantum circuit design by proposing two novel approaches for incorporating quantum advantage metrics into the fitness function of genetic algorithms.1 We evaluate our approaches based on the Bernstein-Vazirani Problem and the Unstructured Database Search Problem as test cases. The results demonstrate that our approaches not only improve the convergence speed of the genetic algorithm but also produce circuits comparable to expert-designed solutions. Our findings suggest that automated quantum circuit design using genetic algorithms that incorporate a measure of quantum advantage is a promising approach to accelerating the development of quantum algorithms.