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Journal of Physics Conference Series

Designing quantum gates using the genetic algorithm

K. S. Kumar, Gheorghe Sorin Paraoanu

Published Dec 17, 2012• 0 citations
Publisher

Abstract

We demonstrate the usage of Genetic Algorithm (GA) to tailor the radio frequency pulses for producing unitary transformations in qubit systems. We find that the initial population converges to the optimal solution after 10 generations, for a one segment pulse corresponding to single qubit Hadamard gate. For a two qubit CNOT gate, we see the population convergence for a two segment pulse after 150 generations. This demonstrates that the method is suitable for designing quantum gates.

DOI
10.1088/1742-6596/400/2/022101

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We demonstrate the usage of Genetic Algorithm (GA) to tailor the radio frequency pulses for producing unitary transformations in qubit systems. We find that the initial population converges to the optimal solution after 10 generations, for a one segment pulse corresponding to single qubit Hadamard gate. For a two qubit CNOT gate, we see the population convergence for a two segment pulse after 150 generations. This demonstrates that the method is suitable for designing quantum gates.
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Genetic quantum algorithms (GQA) are population based evolutionary algorithms that imitate quantum physics by introducing quantum bits for a basic probabilistic genotypic representation and hence better population diversity, and quantum gates for evolving the population of solutions. While quantum inspired gates play an important role in the evolutionary process, there is no specific method for their design, i.e. they are mostly developed through ad hoc procedures. Here, we propose a multi-objective meta-level GQA in order to determine parameters of QG which is applicable for a wide variety of optimization problems. Specifically, a two-layer GQA is constructed, in which the lower layer's objective is to optimize the four junction types: Dejong, Peak, Easoms, and Griewank. And the higher layer's objective is to determine optimal parameters for QG that helps the proposed algorithm find best solutions. GQA optimization performance, with optimized parameter of QG is compared with GA on several benchmark problems and the superiority of the proposed method is statistically shown.
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.
We develop a new class of genetic algorithm that computationally determines efficient pulse sequences to implement a quantum gate U in a three-qubit system. The method is shown to be quite general, and the same algorithm can be used to derive efficient sequences for a variety of target matrices. We demonstrate this by implementing the inversion-on-equality gate efficiently when the spin-spin coupling constants J12=J23=JJ_{12}=J_{23}=JJ12​=J23​=J and J13=0J_{13}=0J13​=0. We also propose new pulse sequences to implement the Parity gate and Fanout gate, which are about 50% more efficient than the previous best efforts. Moreover, these sequences are shown to require significantly less RF power for their implementation. The proposed algorithm introduces several new features in the conventional genetic algorithm framework. We use matrices instead of linear chains, and the columns of these matrices have a well defined hierarchy. The algorithm is a genetic algorithm coupled to a fast local optimizer, and is hence a hybrid GA. It shows fast convergence, and running on a MATLAB platform takes about 20 minutes on a standard personal computer to derive efficient pulse sequences for any target 8X8 matrix UUU.
This paper shows how to design efficient quantum multiplexer circuit borrowed from classical computer design. The design will show that it is composed of some Toffole gates or C 2 NOT gate and some two input CNOT gates. Every C 2 NOT gate is synthesized and optimized by applying the genetic algorithm to get the best possible combination for the design of these gate circuits. gate. It is a three input gate. The first two inputs are the controlled inputs and the third one is the target input. This gate has a 3-bit input and output. If the first two bits are set, it flips the third bit. Following is a table over the input and output bits: Keywords:
Aiming at the issue that quantum genetic algorithm is not suitable for continuons function optimization,an improved quantum genetic algorithm is proposed.This algorithm directly compares the quantum chromosomes with the current best solution to determine the rotating angle of the rotating gate.Every individual in population evolves with different rates to complete local search and global search simultaneously.Mutation operation is used to prevent the premature convergence.After analyzing the algorithm and its global convergence,this algorithm is applied to solve the function extremum and to optimize the PID controller parameters,and it is compared with the standard genetic algorithm and the quantum genetic algorithm.Experimental results illustrate that the proposed algorithm has better performance.