2019/09/24 by Jerimiah Wright, Wright, Jerimiah
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Atomic orbital #Chemical Physics (physics.chem-ph) #Chemistry #Complexity and Algorithms in Graphs #Computational chemistry #Cryptography and Data Security #Emerging Technologies (cs.ET) #FOS: Computer and information sciences #FOS: Physical sciences #Hamiltonian (control theory) #Linear combination of atomic orbitals #Mathematics #Molecular orbital #Molecular physics #Molecule #Pauli exclusion principle #Physics #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum chemistry #Quantum mechanics #Statistical physics #cs.ET #physics.chem-ph #quant-ph
paper · pdf · doi:10.48550/arxiv.1909.11146
published in arXiv (Cornell University) (Cornell University) · 10 pages, 4 figures
arxiv created 2019/09/24 · openalex publication_date 2019/09/24 · arxiv updated 2019/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this experiment was to use the known analytical techniques to study the creation, simulation, and measurements of molecular Hamiltonians. The techniques used consisted of the Linear Combination of Atomic Orbitals (LCAO), the Linear Combination of Unitaries (LCU), and the Phase Estimation Algorithm (PEA). The molecules studied were H2 with and without spin, as well as He2 without spin. Hamiltonians were created under the LCAO basis, and reconstructed using the Jordan-Winger transform in order to create a linear combination of Pauli spin operators. The lengths of each molecular Hamiltonian greatly increased from the H2 without spin, to He2. This resulted in a reduced ability to simulate the Hamiltonians under ideal conditions. Thus, only low orders of l = 1 and l = 2 were used when expanding the Hamiltonian in accordance to the LCU method of simulation. The resulting Hamiltonians were measured using PEA, and plotted against function of (2π(K))/(N) and the probability distribution of each register. The resolution of the graph was dependent on the amount of registers, N, being used. However, the reduction of order hardly changed the image of the H2 graphs. Qualitative comparisons between the three molecules were drawn.