Evolving quantum circuits

François Chapeau‐Blondeau

M. Lukac, Marek A. Perkowski

In this paper we focus on a general approach of using genetic algorithm (GA) to evolve Quantum circuits (QC). We propose a generic GA to evolve arbitrary quantum. circuit specified by a (target) unitary matrix as well as a specific encoding that reduces the time of calculating the resultant unitary matrices of chromosomes. We demonstrate that, in contrast to previous approaches, our encoding allows synthesis of small quantum circuits of arbitrary type, using standard genetic operators.

Taro Yabuki, Hitoshi Iba

We propose a method to apply genetic algorithms to the quantum circuitdesign. We show by experiments that without any deep knowledge of the problem it is possible to evolve a circuit for the quantum teleportation simpler than ever known.

Landry Bretheau

Margareta Vamos

André Leier

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.