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Genetic and Evolutionary Computation Conference Companion (GECCO Companion)

An algorithm for evolving multiple quantum operators for arbitrary quantum computational problems

Walter O. Krawec

Published Jul 11, 2014• 5 citations
Publisher

Abstract

We design and analyze a real-coded genetic algorithm for the use in evolving collections of quantum unitary operators (not circuits) which act on pure or mixed states over arbitrary quantum systems while interacting with fixed, problem specific operators (e.g., oracle calls) and intermediate partial measurements. Our algorithm is general enough so as to allow its application to multiple, very different, areas of quantum computation research.

DOI
10.1145/2598394.2598408

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arXiv:cs/0403003•Mar 4, 2004•20 citations
We design and analyze a real-coded genetic algorithm for the use in evolving collections of quantum unitary operators (not circuits) which act on pure or mixed states over arbitrary quantum systems while interacting with fixed, problem specific operators (e.g., oracle calls) and intermediate partial measurements. Our algorithm is general enough so as to allow its application to multiple, very different, areas of quantum computation research.
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.
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.
Automatic quantum circuit design is motivated by the difficulties in manual design, because quantum algorithms are highly non-intuitive and practical quantum computer hardware is not yet available. Thus, quantum computers have to be simulated on classical hardware which naturally entails an exponential growth of computational costs and allows only to simulate small quantum systems, i. e., with only few qubits. Huge search spaces render evolutionary approaches nearly unable to achieve breakthrough solutions in the development of new quantum algorithms. Consequently, at present we must be content to evolve essentially already existing (black-box) quantum algorithms. This thesis presents empirical results on the evolution of quantum circuits using genetic programming. For that purpose, a linear and a linear-tree GP system (allowing intermediate measurements) with integrated quantum computer simulator were implemented. Their practicality in evolving quantum circuits is shown in different experiments for 1-SAT (solutions act like Hogg's algorithm) and the Deutsch-Jozsa problem. These experiments confirm that the evolution of quantum circuits is practically feasible only for sufficiently small problem instances. In this context, scalability and the detection of scalability becomes very important. It is shown that scalable quantum circuits are evolvable to a certain degree: a general quantum circuit can be inferred manually from the evolved solutions for small instances of the given problem. Besides, further experiments indicate that 're-evolution' is effective for the evolution of scalable quantum circuits. With this method the start population of a problem instance is inoculated with evolved solutions for a smaller problem instance. Furthermore, investigations of fitness landscapes and selection strategies are made, with the aim of improving the efficiency of evolutionary search. A notable result is that using the crossover operator damages rather than benefits evolution of quantum circuits.
In this thesis we present a genetic programming scheme for evolving quantum programs in the form of arbitrary unitary operators. Expanding on the work done by Hutsell and Greenwood, and later by Krawec in developing unitary operator evolution schemes, we present an alternative representation for unitary operators which has a better search topology than the representations used in these previous implementations. This alternative representation is tested on a general unitary evolution problem, and displays better convergence than previously implemented representations.
Recently, researchers have applied genetic algorithms (GAs) to address some problems in quantum computation. Also, there has been some works in the designing of genetic algorithms based on quantum theoretical concepts and techniques. The so called Quantum Evolutionary Programming has two major sub-areas: Quantum Inspired Genetic Algorithms (QIGAs) and Quantum Genetic Algorithms (QGAs). The former adopts qubit chromosomes as representations and employs quantum gates for the search of the best solution. The later tries to solve a key question in this field: what GAs will look like as an implementation on quantum hardware? As we shall see, there is not a complete answer for this question. An important point for QGAs is to build a quantum algorithm that takes advantage of both the GA and quantum computing parallelism as well as true randomness provided by quantum computers. In the first part of this paper we present a survey of the main works in GAs plus quantum computing including also our works in this area. Henceforth, we review some basic concepts in quantum computation and GAs and emphasize their inherent parallelism. Next, we review the application of GAs for learning quantum operators and circuit design. Then, quantum evolutionary programming is considered. Finally, we present our current research in this field and some perspectives.