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IEEE Congress on Evolutionary Computation (CEC)

Applying evolutionary techniques to quantum computing problems

Steven R. Hutsell, Garrison W. Greenwood

Published Sep 1, 2007• 16 citations
Publisher

Abstract

A new approach based on Evolution Strategies (ES) is proposed to evolve quantum unitary operators which represent the computational algorithm a quantum computer would perform to solve an arbitrary problem. This approach has superior attributes over previous endeavors by using real valued vectors and not limited to a predefined set of quantum gates. We show this method can be used to solve a variety of key problems from evolving simple quantum gates, quantum oracles, to generalized problem instances. This method is highly extensible and useful for propagating future research of quantum unitary operator development.

DOI
10.1109/cec.2007.4425003

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A new approach based on Evolution Strategies (ES) is proposed to evolve quantum unitary operators which represent the computational algorithm a quantum computer would perform to solve an arbitrary problem. This approach has superior attributes over previous endeavors by using real valued vectors and not limited to a predefined set of quantum gates. We show this method can be used to solve a variety of key problems from evolving simple quantum gates, quantum oracles, to generalized problem instances. This method is highly extensible and useful for propagating future research of quantum unitary operator development.
This paper presents a comparative study regarding the evolutionary design of quantum operators in the form of unitary matrices. Three different techniques allowing the generation of unitary matrices are investigated whose parameters are tuned by means of evolutionary algorithms. Such problem may be considered as a numerical optimisation task because the unitary matrices are represented by complex numbers with real-valued coefficients. Specifically, Genetic Algorithm and Evolution Strategy are applied, each in four different setups, and evaluated on three case studies: the 2-qubit Controlled-NOT gate, 3-qubit entanglement operator and 4-qubit detector of an element with the maximum amplitude. The evolutionary algorithms in combination with the given representation techniques are evaluated in order to determine the abilities of various experimental setups to solve the given tasks. The main contribution is the utilisation of QR decomposition, a technique for generating unitary matrices from theoretically any sequence of complex numbers, that has been applied for the first time in this paper for the evolution of quantum operators. It will be demonstrated that the QR decomposition exhibits a good performance especially in solving more complex quantum operators in comparison with other representations.
A comparative study is presented regarding the evolutionary design of quantum operators in the form of unitary matrices.A comparative study is presented regarding the evolutionary design of quantum operators in the form of unitary matrices. Three existing techniques (representations) which allow generating unitary matrices are used in various evolutionary algorithms in order to optimize their coefficients. The objective is to obtain as precise quantum operators (the resulting unitary matrices) as possible for given quantum transformations. Ordinary evolution strategy, self-adaptive evolution strategy and differential evolution are applied with various settings as the optimization algorithms for the quantum operators. These algorithms are evaluated on the tasks of designing quantum operators for the 3-qubit and 4-qubit maximum amplitude detector and a solver of a logic function of three variables in conjunctive normal form. These tasks require unitary matrices of various sizes. It will be demonstrated that the self-adaptive evolution strategy and differential evolution are able to produce remarkably better results than the ordinary evolution strategy. Moreover, the results can be improved by selecting a proper settings for the evolution as presented by a comparative evaluation.
We propose a genetic-algorithm-based method to find the unitary transformations for any desired quantum computation. We formulate a simple genetic algorithm by introducing the “genetic parameter vector” of the unitary transformations to be found. In the genetic algorithm process, all components of the genetic parameter vectors are supposed to evolve to the solution parameters of the unitary transformations. We apply our method to find the optimal unitary transformations and to generalize the corresponding quantum algorithms for a realistic problem, the one-bit oracle decision problem, or the often-called Deutsch problem. By numerical simulations, we can faithfully find the appropriate unitary transformations to solve the problem by using our method. We analyze the quantum algorithms identified by the found unitary transformations and generalize the variant models of the original Deutsch’s algorithm.
A novel evolutionary algorithm based on quantum computing concepts is applied to engineering optimization problems. Quantum computing mimics behavior of atoms in processing information. Quantum inspired algorithm is a concept, which employs certain elements of quantum computing to use in a wider class of search and optimization problems. The main parts of a quantum-inspired algorithm are the qubits (quantum equivalent of bits) and the quantum gates. Qubits hold the information in a superposition of all the states, while the quantum gates evolve the qubit to achieve the desired objective, which is, in optimization the maximum or the minimum. The paper addresses the ability of the Quantum-Inspired Evolution Algorithm (QIEA) to solve practical engineering optimization problems. QIEA, which is developed by authors, is based on their previous work and it is extended to acquire the floating-point representation of the information. The RQIEA is tested on a four benchmark engineering optimization problems. The results showed that the new algorithm has the ability to compete and even overcome other well known methods.
We investigate two modified Quantum Evolutionary methods for solving real value problems. The Quantum Inspired Evolutionary Algorithms (QIEA) were originally used for solving binary encoded problems and their signature features follow superposition of multiple states on a quantum bit and a rotation gate. In order to apply this paradigm to real value problems, we propose two quantum methods Half Significant Bit (HSB) and Stepwise Real QEA (SRQEA), developed using binary and real encoding respectively, while keeping close to the original quantum computing metaphor. We evaluate our approaches against sets of multimodal mathematical test functions and real world problems, using five performance metrics and include comparisons to published results. We report the issues encountered while implementing some of the published real QIEA techniques. Our methods focus on introducing and implementing new rotation gate operators used for evolution, including a novel mechanism for preventing premature convergence in the binary algorithm. The applied performance metrics show superior results for our quantum methods on most of the test problems (especially for the more complex and challenging ones), demonstrating faster convergence and accuracy.