2021/12/02 by Ivana Miháliková, Martin Friák, Matej Pivoluska +4
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Benchmark (surveying) #Computer science #Excited state #Ground state #Hamiltonian (control theory) #Mathematical optimization #Mathematics #Perturbation theory (quantum mechanics) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum computer #Quantum mechanics #Qubit #Series (stratigraphy) #Simultaneous perturbation stochastic approximation #Statistical physics #Stochastic process #quant-ph
paper · pdf · doi:10.3390/molecules27030597
17 pages
arxiv created 2021/12/02 · openalex publication_date 2022/01/18 · arxiv updated 2022/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quantum computers are reaching one crucial milestone after another. Motivated by their progress in quantum chemistry, we performed an extensive series of simulations of quantum-computer runs that were aimed at inspecting the best-practice aspects of these calculations. In order to compare the performance of different setups, the ground-state energy of the hydrogen molecule was chosen as a benchmark for which the exact solution exists in the literature. Applying the variational quantum eigensolver (VQE) to a qubit Hamiltonian obtained by the Bravyi-Kitaev transformation, we analyzed the impact of various computational technicalities. These included (i) the choice of the optimization methods, (ii) the architecture of the quantum circuits, as well as (iii) the different types of noise when simulating real quantum processors. On these, we eventually performed a series of experimental runs as a complement to our simulations. The simultaneous perturbation stochastic approximation (SPSA) and constrained optimization by linear approximation (COBYLA) optimization methods clearly outperformed the Nelder-Mead and Powell methods. The results obtained when using the Ry variational form were better than those obtained when the RyRz form was used. The choice of an optimum entangling layer was sensitively interlinked with the choice of the optimization method. The circular entangling layer was found to worsen the performance of the COBYLA method, while the full-entangling layer improved it. All four optimization methods sometimes led to an energy that corresponded to an excited state rather than the ground state. We also show that a similarity analysis of measured probabilities can provide a useful insight.