An Application Of Quantum Computing Into Studying The Nucleon Structure

In recently,quantum computing is one of the hot research topics in many fields.Quantum computing is a new computing theory,based on the quantum mechanics.Since the computing conforms to quantum mechanism,to distinguish from the computing that many computers currently use,we call it quantum computing.In the thesis,we apply quantum computing into the study of nucleon structure and summerize and develop the methods that calculate correlation functions and simulate hadron.Taking the advantage of quantum computing in real-time evolution,we solve the problem that classical lattice theory can’t.Using quantum approximate optimization algorithm and variational quantum eigensolver,et al,we simulate hadron with energy level,charge and momentum.The nucleon structure is an important research in high-energy nuclear physics.In nucleon,strong interaction domains,described by QCD.However,the non-perturbative at low energy scale prevents us deducing a correct analytical result from perturbative QCD,so numerical solution becomes a practical way,such as lattice QCD theory and quantum computing.Lattice QCD is proved to be a successful theory by experiments while quantum computing is still in an early,rudimentary stage,but,with fast development and wide application.Compared with lattice QCD,one of quantum-computing’s superiority is real-time evolution,that quantum computing is able to do real-time dynamics evolution,because quantum computing is exactly based on the quantum mechanics and therefore,it can perform such quantum process directly.In the thesis,we focus on 3 quantities that can describe nucleon structure,namely meson π0’s PDF,LCDA and GPD.To obtain these results,it’s key to calculate the correlation function correspondingly,for it contains the information about nucleon structure.Before starting calculate this function,we need to build the quantum circuits that reprecent the Dirac fields and time evolution operators,and to simulate and produce required hadron state.Using Staggered-Fermion approach and Jordan-Wigner transform,et al,we discretize Dirac fields and build the quantum circuits to reprecent the fields.Using Trotterization formula and other techiques,we build the quantum circuits to realize the real-time evolution.By using VQE algorithm and other algorithms,we simulate and produce required hadron state.Especially,based on the preceding works,we develop a method to produce hadron state with momentum using even-lattice translation.Finally,we introduce an ancillary qubit and input the hadron state we produced to the quantum circuits we build.Under control of the ancillary qubit,we can finally get the result of correlation function by measuring the ancillary qubit,because the quantum algorithm encodes the result of correlation function into an ancillary qubit.Through the study of the thesis,we develop a method that produce hadron state with momentum,introduce how to calculate PDF,LCDA and GPD with quantum computing and provide more possibilities for applying quantum computing into the study of nucleon structure.In the thesis,there are 5 sections,organized by following orders:In section 1,we will introduce the basic knowledge about studying nucleon structure,such as parton theory,LCDA and so on.We will also introduce a theoretical model we use,1+1 dimensional NJL model;In section 2,we will introduce some basic knowledge about quantum computing that we should know before next section,including qubit,quantum gate and quantum circuit;In section 3,based on the section 2,we introduce our works:build the quantum circuits that can calculate 2-point correlation function and simulate hadron state.Especially based on the preceding works that simulate hadron state with 0 charge,we develop a method that can simulate and produce hadron state with momentum;In section 4,based on the previous 3 sections,we apply quantum computing into calculating meson π0’s PDF,LCDA and GPD.Especially,inspired by some preceding works about calculating PDF and LCD A,we obtain the result of GPD;In the final section,we will make a brief summary of our works.