Robust Variational Circuit Ansatz Through Genetic Algorithm

Quantum simulation and quantum computation are challenging for classical computers because of the high computational cost.In comparison,quantum computers are good at dealing with these problems,but there are serious limitations in the near-term noisy quantum devices.The imperfections of quantum gate implementation will limit the scalability of quantum circuits.In recent years,variational quantum algorithms are proposed as powerful methods implementable on the noisy intermediate-scale quantum devices.Nevertheless,challenges still exist including trainability,accuracy,and efficiency for these variational quantum algorithms.This thesis focuses how to execute the variational quantum algorithms on noisy near-term quantum devices in a reliable and robust way.My work consists of two parts.The first part introduces the variational quantum eigensolver on near-term quantum devices.Variational quantum eigensolver is a variational quantum algorithm.Variational quantum algorithms use a classical optimizer to train parametric quantum ansatz.This means that variational quantum algorithms are hybrid algorithms of classical-quantum.In this part,we propose a quantum circuit evolutionary algorithm based on the classical evolutionary algorithm to generate a robust quantum circuit structure.This thsis encodes the quantum circuit structure into the genomes,change the genome structures through mutation and crossover operations,and select the circuit structure with the best performance.In the selection process,the algorithm use a strategy of robust quantum control and a classical optimizer to optimize the parameters of quantum ansatz;then,algorithm can achieve the optimal performance of each genome.After the evolutionary process,algorithm can finally obtain the robust quantum circuit in the noisy near-term quantum device.The comparative analysis shows that the quantum circuits trained by a classical evolutionary algorithm are shallower than the well-used hardware effective ansatz and get lower energy.Although the algorithm in this project will cost a huge of classical and quantum resources,in quantum chemistry.This thesis is more concerned about the accuracy of the energy forming the bond,and in this thesis proposed system,such algorithms are reliably implemented on noisy near-term quantum computers.The second part of my work deals with solving machine-learning classification problems,on a noisy near-term quantum device.Due to the influence of quantum incoherent and coherent noises on near-term quantum equipment,the quantum classification tasks can not be solved in a perfect way.Therefore,this work hopes to use combinations of shallow quantum variational circuits to overcome noise effect.This thesis will use an idea from classical machine learning to improve the accuracy of quantum classification tasks.Through the adder principle,the adaboost method linearly combines shallow variational quantum circuits to form a strong classifier.Such a strong classifier will achieve a good performance against noise.Based on the fact that the training error of two classification tasks decreases exponentially with the number of weak classifiers in the combination,I find that the training error of multi-classification decreases exponentially with the number of weak classifiers.The quantum algorithms studied in this thesis are the ones implemented on a nearterm noisy quantum computer.The first algorithm is concerned with how to generate shallow quantum circuit structures.The second algorithm is concerned with whether the shallow quantum circuit structure has robust advantages in noisy quantum computers.These two algorithms developed in this work provide new routes to solve the eigenvalue problem and the classification task on a noisy quantum device.Further,this work provides a general framework on how to design robust quantum circuits and how to improve the the performance of quantum classification on near-term quantum computers.