Study On Quantum Support Vector Machine Algorithm

Support vector machine(SVM)algorithm is a machine learning method based on statistical learning theory and principle of structural risk minimization,widely used in pattern recognition,regression analysis,probability density estimation and other fields.It has solid theoretical foundation,simple mathematical model and strong generalization ability.Besides,SVM can effectively solve high-dimensional problems and nonlinear problems.Since the statistical learning theory mainly studies the problems with small sample size,SVM needs too long learning time and excessive storage space when the training data size is large.Quantum support vector machine(QSVM)algorithm can efficaciously solve these problems.In this paper,a general logic circuit is designed based on the study and research of QSVM.The general logic circuit is consisted of four parts,the first part uses phase estimation algorithm to estimate the eigenvalues of QSVM matrix and decomposes the operator corresponding to QSVM matrix.In the process of performing Hamiltonian simulation on the decomposed operators,the kernel matrix can be quickly calculated by the reduced density operator of the composite system,achieving exponential acceleration in time complexity compare with the classical method.The second part encodes the reciprocals of the eigenvalues of QSVM matrix to the computational basis by the method to calculate the quantum state of the reciprocals of the eigenvalues,and then the computational basis control the revolving gate to act on the auxiliary qubit for obtaining the quantum state of QSVM parameters.The quantum state which represents QSVM parameters is used to control the quantization of the training data in the third part,and QSVM parameters are encoded in the amplitude for the quantum state of the support vectors.The circuit preparing the quantum state of the test data is used to calculate the inner product among the feature vectors in the fourth part,which obtains the classification decision function value of the test samples.Finally,according to the general logic circuit of QSVM,a simulation experiment is conducted to classify iris samples.The experimental results are compared with the actual category of the samples to verify the efficiency and correctness of the general logic circuit.