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IEEE Congress on Evolutionary Computation (CEC)

Evolving quantum circuits using genetic programming

Benjamin I. P. Rubinstein

Published Nov 13, 2002• 67 citations
Publisher

Abstract

The paper presents a new representation and corresponding set of genetic operators for a scheme to evolve quantum circuits with various properties. The scheme is a variant on the techniques of genetic programming and genetic algorithms, having components borrowed from each. By recognising the foundation of a quantum circuit as being a collection of gates, each operating on various categories of qubits and each taking parameters, the scheme can successfully search for most circuits. The algorithm is applied to the problem of entanglement production.

DOI
10.1109/cec.2001.934383

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The paper presents a new representation and corresponding set of genetic operators for a scheme to evolve quantum circuits with various properties. The scheme is a variant on the techniques of genetic programming and genetic algorithms, having components borrowed from each. By recognising the foundation of a quantum circuit as being a collection of gates, each operating on various categories of qubits and each taking parameters, the scheme can successfully search for most circuits. The algorithm is applied to the problem of entanglement production.
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Research in quantum technology has shown that quantum computers can provide dramatic advantages over classical computers for some problems. The efficiency of quantum computing is considered to become so significant that the study of quantum algorithms has attracted widespread interest. Development of quantum algorithms and circuits is difficult for a human researcher, so automatic induction of computer programs by means of genetic programming, which uses almost no auxiliary information on the search space, proved to be useful in generating new quantum algorithms. This approach takes advantage of the intrinsic parallelism of the genetic algorithm and quantum computing parallelism. The paper begins with a brief review on some basic concepts in genetic algorithms and quantum computation. Next, it describes an application of genetic programming for evolving quantum computing circuits.
Quantum programs are difficult for humans to develop due to their complex semantics that are rooted in quantum physics. It is therefore preferable to write specifications and then use techniques such as genetic programming (GP) to generate quantum programs instead. We present a new genetic programming system for quantum circuits which can evolve solutions to the full-adder and quantum Fourier transform problems in fewer generations than previous work, despite using a general set of gates. This means that it is no longer required to have any previous knowledge of the solution and choose a specialised gate set based on it.
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.
Quantum computing is a new way of data processing based on the concept of quantum mechanics. Quantum circuit design is a process of converting a quantum gate to a series of basic gates and is divided into two general categories based on the decomposition and composition. In the second group, using evolutionary algorithms and especially genetic algorithms, multiplication of matrix gates was used to achieve the final characteristic of quantum circuit. Genetic programming is a subfield of evolutionary computing in which computer programs evolve to solve studied problems. In past research that has been done in the field of quantum circuits design, only one cost metrics (usually quantum cost) has been investigated. In this paper for the first time, a multi-objective approach has been provided to design quantum circuits using genetic programming that considers the depth and the cost of nearest neighbor metrics in addition to quantum cost metric. Another innovation of this article is the use of two-step fitness function and taking into account the equivalence of global phase in quantum gates. The results show that the proposed method is able to find a good answer in a short time.