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High speed genetic algorithms in quantum logic synthesis: Low level parallelization vs. representation

Martin Lukáč, Michitaka Kameyama, D. Michael Miller, Marek A. Perkowski

Published Dec 28, 2012• 7 citations
OpenAlex

Abstract

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.

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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.
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.
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 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.
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 an evolutionary approach to the quantum symbolic logic synthesis. We use a genetic algorithm to synthesize quantum circuits from examples, allowing to synthesize functions that are both completely and incompletely specified. The symbolic synthesis is implemented in the GA so as to verify our approach. The Occam Razor principle, fundamental to inductive learning as well as to logic synthesis, is satisfied in this approach by seeking circuits of reduced complexity. The GA is tested on a set of benchmark functions representing single output quantum circuits as well as multiple entangled-qubit state generators.
Reversible quantum logic synthesis is to study given quantum gates and quantum circuits of the constraints and limitations and find the smallest or smaller quantum cost to achieve the desired quantum logic circuits.The quantum logic gate functions of the matrix is indicated by the mathematical model. The synthesis and optimization are achieved simultaneously by the genetic algorithm as global search tool. Genetic algorithm is applied to quantum reversible logic synthesis.The fourth-order quantum circuit experiment has achieved good results,and further analysis of this method in high-level synthesis of quantum circuits and its application is completed.