Research On Quantum Algorithms For Molecular Spectroscopy Problems

With the advent of the first electronic computers,scientific computing based on clas-sical computing flourished.Yet many intriguing questions cannot be addressed in classical computers,such as how the computational complexity of simulating a quantum system,such as a molecular system,on a classical computer grows exponentially as the size of the system being simulated increases.Quantum chemistry is an important discipline that uses quantum theory and methods to study molecular structures,chemical reactions,and so on,and it is of great application in the fields of drug R and D and exploring new materials.An important research direction in quantum chemistry is the calculation of molecular energy spectra,the accurate calculation of molecular energy spectra is a very complicated work,and many high-precision approximation methods have been developed in recent years,but their complexity is indeed prohibitive for molecular systems with large systems.The advent of quantum computing has brought new avenues to solve this challenging and com-plex problem.Calculation of molecular energy spectra on noisy small-to medium-scale quantum computers（NISQ）is highly possible relying on the recently emerging variational quantum eigensolver solution unitary coupled cluster（VQE-UCC）algorithm.However,vqe-ucc algorithms still need to reduce the complexity when modeling macromolecules due to the limitation of the number of qubit and coherence time in quantum computers,which cannot implement excessively long quantum lines.The current circuit depth of the variational quantum eigensolution algorithm based on the unitary coupled cluster method is still too high,which is unfavorable for the sim-ulation on existing nisq devices.Therefore,we have developed a novel unitary coupled cluster method singlet pair excited cluster method（spucc）based on simulated symmetry of molecular systems,which reduces the number of physically unnecessary excitation opera-tors,reduces the number of optimized parameters,and approximates the double excitation operator involved to a single excitation operator and the pair excitation operator involved to two indexes combined.Using the variational quantum eigensolution algorithm based on the spucc method to calculate the ground state of molecules,the computational com-plexity is significantly reduced,and the number of quantum gates is greatly reduced.With this method,we calculated a plot of the energy of the ground state of the molecule H₂O as a function of bond length,in substantial agreement with the true results.The energy profiles of our ground state and excited state of molecule H₄as a function of bond angle were calculated simultaneously,resulting in good overcurves of its point group junction structures from C_2vto C_4vto C_2v,which were consistent with the results after accurate diagonalization,which verified the accuracy of this coupled cluster method.We also per-formed calculations on the strongly bonded molecule N₂,demonstrating the superiority of this method over some of the current coupled cluster method variants.Finally we propose a simple experimental scheme based on the pre-existing theoretical results and the energy level structure of the ion trap.We believe that our methods and conclusions are expected to advance the development of quantum chemical simulations.