By exploiting a quantum algorithm to help optimize the underlying objective function, we obtained an efficient procedure for the calculation of the electronic ground state energy for a small molecule system. In chapter 3, we report a hybrid quantum algorithm employing a restricted Boltzmann machine to obtain accurate molecular potential energy surfaces. This demonstrates that one can map the molecular Hamiltonian to an Ising-type Hamiltonian which could easily be implemented on currently available quantum hardware. The numerical simulation results of the transformed Hamiltonian for H 2, He 2, HeH +, and LiH molecules match the exact numerical calculations of the original Hamiltonian. We also design an algorithm to use the transformed Hamiltonian to obtain the approximating ground energy of the original Hamiltonian. Then introduce ancilla qubits to transform the diagonal Hamiltonian to an Ising-type Hamiltonian.
The whole mapping is enabled by first enlarging the qubits space to transform the electronic structure Hamiltonian to a diagonal Hamiltonian. In chapter 2, we show an approximating mapping between the electronic structure Hamiltonian and the Ising Hamiltonian. We also give a general review about electronic structure calculations on quantum computer. In chapter 1 we present a general introduction of quantum computer, including a brief introduction of two quantum computing model: gate model and quantum annealing model.
This dissertation contains four projects: transforming electronic structure Hamiltonian to approximating Ising-type Hamiltonian to enable electronic structure calculations by quantum annealing, quantum-assisted restricted Boltzmann machine for electronic structure calculations, hybrid quantum classical neural network for calculating ground state energies of molecules and qubit coupled cluster single and double excitations variational quantum eigensolver for electronic structure.
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