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arXiv:1003.3142

Constructing quantum circuits for maximally entangled multi-qubit states using the genetic algorithm

Zheyong Fan, Hugo de GARIS, Ben Goertzel, Zhongzhou Ren, Hua-Bi Zeng

Published Mar 16, 2010• 1 citation
arXivHTMLPDF

Abstract

Numerical optimization methods such as hillclimbing and simulated annealing have been applied to search for highly entangled multi-qubit states. Here the genetic algorithm is applied to this optimization problem -- to search not only for highly entangled states, but also for the corresponding quantum circuits creating these states. Simple quantum circuits for maximally (highly) entangled states are discovered for 3, 4, 5, and 6-qubit systems; and extension of the method to systems with more qubits is discussed. Among other results we have found explicit quantum circuits for maximally entangled 5 and 6-qubit circuits, with only 8 and 13 quantum gates respectively. One significant advantage of our method over previous ones is that it allows very simple construction of quantum circuits based on the quantum states found.

DOI
10.48550/arxiv.1003.3142

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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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