Research On Variational Quantum Algorithm And Its Optimization Technology For Solving Nonlinear Equations

It has been one of the hot research issues in the field of quantum computing to the large integer factorization by quantum computer since shor's algorithm for polynomial time complexity of factorization has been proposed.Due to the current difficulties of qubits that are difficult to substantially isolate noise and quantum error correction is still immature,quantum computing will undergo a development process from noisy intermediate-scale quantum computers to universal fault-tolerant quantum computers.This makes people to find new alternative solutions.One of the methods is to factorize large biprimes by using the principle of quantum mechanics,transform the factorization problem into a combinatorial optimization problem,and further equivalent to solving a set of nonlinear equations,and a typical algorithm is variational quantum algorithm.Quantum neural network is a kind of variational learning paradigm with good performance,which can be applied to quantum processors.Limited by the current quantum computing hardware level,quantum models need to work with classical coprocessor together.Therefore,this paper proposes to focuse on the quantum neural network based variational quantum algorithm,and proposes an efficient variational quantum algorithm based on the detailed analysis of the existing algorithms as follows:(1)Variational quantum algorithm analysis and optimization:Combining the current quantum computer hardware level and integer factorization quantum algorithms,this paper proposes a "classical + quantum" hybrid solution.This scheme first adopts classical methods and corresponding rules in the preprocessing step to simplify the nonlinear equations,which is used to reduce the number of qubits needed for the cost Hamiltonian.Then the variational quantum algorithm is used to find the approximate ground state of the cost Hamiltonian,which encodes the solution of the nonlinear equations.The program was verified on the IBM QX4 quantum machine,and the results showed that this hybrid solution can effectively reduce the quantum resources required to solve the nonlinear equations.(2)Variational quantum algorithm model based on quantum neural network TFQ-VQA: Aiming at the problem that the quantum circuit depth of the variational quantum algorithm increases with the number of iterations,this paper proposes a variable quantum algorithm model based on quantum neural networks TFQ-VQA.This model combines quantum neural networks with classical neural networks,and trains the classical recurrent neural network to assist the quantum learning process by observing the correlation between the parameters of different depths of VQA,and initializes other optimizers based on the parameter values given by the classical neural network.The model finds the approximate optimal parameters in less queries on the cost function of the variational quantum algorithm.(3)Two-level optimization method based on TFQ-VQA: By observing the correlation between the parameters of the variable component algorithm at different depths,this paper proposes a two-level optimization method based on the quantum model TFQ-VQA.In the first stage,the instance of depth of 1 is optimized for the target problem.In the second stage,the target depth,the pre-trained quantum model,and the optimal parameter values of depth 1 are used to predict the initial value of the control parameter of the target depth instance to accelerate the execution of the variable component algorithm.Results of experiment show that the number of optimization iterations required has been significantly reduced for the model to achieve a given accuracy result.