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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Quantum computing approach to non-relativistic and relativistic molecular energy calculations
 Veis, Libor ; Pittner, Jiří (advisor) ; Skála, Lubomír (referee) ; Nagaj, Daniel (referee)
Quantum computers are appealing for their ability to solve some tasks much faster than their classical counterparts. In fact, they have a potential to perform the full configuration interaction (FCI) energy calculations with a polynomial scaling only. This is in contrast to con- ventional computers where FCI scales exponentially. We provide a detailed description of the quantum version of the FCI method and the results of numerical simulations of the ground and excited state energy calculations of the methylene molecule. We further generalize this method to the relativistic four component regime and show how to efficiently solve the eigenproblem of the Dirac-Coulomb(-Breit) Hamiltonian on a quantum computer. We demonstrate the func- tionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with 3 qubits and 9 or 10 CNOTs, which implement a proof-of-principle relativistic quantum chemical calculation for this molecule and might be suitable for an experimental realization. 1
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Quantum computing algorithms for quantum chemistry
 Višňák, Jakub ; Skála, Lubomír (advisor) ; Čurík, Roman (referee) ; Pittner, Jiří (referee)
Title: Quantum computing algorithms for quantum chemistry Author: Jakub Višňák Abstract: The topic of this study is the simulation of the quantum algorithm for the diagonalization of the matrix representation of the all-electron Dirac-Coulomb hamiltonian of the SbH molecule. Two different limited CI expansions were used to describe both the ground state (X 0+ ) and the first excited doublet (A 1) by simulating the Iterative Phase Estinamtion Algorith (IPEA). In the simulations numerically performed in this work, the "compact mapping" has been employed for the representation of the evolution operator exp(i Hˆ t); in the theoretical part of the work, the "direct mapping" is described as well. The influence of the metodics for choosing the initial eigenvector estimate is studied in both IPEA A and IPEA B variants. For those variants, the success probabilities pm are computed for different single-points on the SbH dissociation curves. The initial eigenvector estimates based on the "CISD(2)" method are found to be sufficient for both studied LCI-expansions up to internuclear distance R  6 a0. The pm dependence on the overlap between the eigenvector in question and its inital estimate - 2 0  is studied the for IPEA B method. The usability of the both variants of the IPEA in possible later calculations is...
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