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Genetic Algorithms for Quantum Circuit Design –Evolving a Simpler Teleportation Circuit–

Taro Yabuki, Hitoshi Iba

Published Jan 1, 2000• 34 citations
OpenAlex

Abstract

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.

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NASA/DoD Conference on Evolvable Hardware•Jun 25, 2003•77 citations
Abstract. In order to design a quantum circuit that performs a desired quantum computation, it is necessary to find a decomposition of the unitary matrix that represents that computation in terms of a sequence of quantum gate operations. To date, such designs have either been found by hand or by exhaustive enumeration of all possible circuit topologjks. In this paper we propose an automated approach to quantum circuit design using search heuristics based on principles abstracted from evolutionary genetics, i.e. using a genetic programming algorithm adapted specially for this problem. We demonstrate the method on the task of discovering quantum circuit designs for quantum teleportation. We show that to find a given known circuit design (one which was hand-crafted by a human), the method considers roughly an order of magnitude fewer designs than naive enumeration. In addition, the method finds novel circuit designs superior to those previously known. 1
Quantum Teleportation is the process of transmitting Quantum information from one place to another by performing Quantum mechanical operations like entanglement, Bell measurement and classical communication.Unlike the commonly used term teleportation, Quantum teleportation involves only transfer of information rather than particles or objects.Quantum teleportation allows transmission of quantum information despite the impossibility of measuring or broadcasting the information to be transmitted.This paper evolves some new simpler Quantum teleportation circuits which use only Quantum entanglement and a set of Hadamard and CNOT gates.Further, each of the circuits performs teleportation even if Alice does not perform measurement on her qubits.Keeping the feasibility of physical realization in mind, circuits using only adjacent CNOT gates along with Hadamard gates have also been constructed.All these circuits have been evolved using Genetic Algorithms which has been designed with appropriate representation and search operations towards faster convergence.
Due to the non- intuitive nature of Quantum algorithms, it becomes difficult for a classically trained person to efficiently construct new ones. So rather than designing new algorithms manually, lately, Genetic algorithms (GA) are being implemented for this purpose. GA is a technique to automatically solve a problem using principles of Darwinian evolution. This has been implemented to explore the possibility of evolving an n-qubit circuit when the circuit matrix has been provided using a set of single, two and three qubit gates. Using a variable length population and universal stochastic selection procedure, a number of possible solution circuits, with different number of gates can be obtained for the same input matrix during different runs of GA. The given algorithm has also been successfully implemented to obtain two and three qubit Boolean circuits using Quantum gates. The results demonstrate the effectiveness of the GA procedure even when the search spaces are large.
This paper applies a standard genetic algorithm to the optimization of the quantum circuits. We propose a new coding scheme, which encodes quantum gates as integers and stores circuit topology information in the position of the integers. The design of the corresponding fitness function and genetic operators are also discussed. The quantum teleportation circuit, a typical quantum computation process, is chosen as our optimization target. Finally, the experiment results are discussed, and an optimized teleportation circuit has been obtained.