Computational chemistry on quantum computers
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Computational chemistry on quantum computers Ground state estimation V. Armaos1,2 · Dimitrios A. Badounas1,3 · Paraskevas Deligiannis1 · Konstantinos Lianos1,4 Received: 20 January 2020 / Accepted: 23 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We present computational chemistry data for small molecules (CO, HCl, F 2 , NH+4 , CH4 , NH3 , H 3 O+ , H 2 O, BeH2 , LiH, OH− , HF, HeH+ , H 2 ), obtained by implementing the unitary coupled cluster method with single and double excitations (UCCSD) on a quantum computer simulator. We have used the variational quantum eigensolver (VQE) algorithm to extract the ground state energies of these molecules. This energy data represents the expected ground state energy that a quantum computer will produce for the given molecules, on the STO-3G basis. Since there is a lot of interest in the implementation of UCCSD on quantum computers, we hope that our work will serve as a benchmark for future experimental implementations. Keywords Quantum computing · Computational chemistry · VQE · UCCSD · NISQ
1 Introduction The most natural application of quantum computers is to simulate quantum mechanical systems [1]. The appearance of quantum algorithms [2–4] and subsequently of quantum processors [5, 6] has made this argument solid enabling quantum computing. Several important problems which are traditionally hard to solve on classical computers can be now addressed on their quantum counterparts [7, 8]. Quantum chemistry is one of the most promising applications of quantum computing. With only a few hundreds of logical qubits, quantum computers seem to outperform classical computers in the determination of molecular energies [9]. Several quantum computation algorithms [10] * V. Armaos [email protected] * Dimitrios A. Badounas [email protected] 1
PiDust, Patras, Greece
2
Laboratory of Atmospheric Physics, Department of Physics, University of Patras, Patras, Greece
3
Department of Material Science, University of Patras, Patras, Greece
4
Department of Computer Engineering and Informatics, University of Patras, Patras, Greece
have been used to estimate the energy of small molecules, however simulations of larger molecules still remain out of reach because of the limitation in the number of qubits and coherence times in noisy intermediate scale quantum (NISQ) devices. Sophisticated methods have been used to reduce the cost of quantum chemistry simulations [11–13], such as hybrid quantum classical (HQC) algorithms [14, 15]. Here we focus on one of these HQC algorithms, the variational quantum eigensolver (VQE) [16]. In this algorithm, the computation is split into several quantum sub-tasks. A classical optimizer controls the experiments performed on the quantum computer to determine the parameters that minimize the expectation value of the Hamiltonian. This is equivalent to finding the eigenvector of the Hamiltonian with the smallest eigenvalue, hence the name of the method. In order to solve quantum chemistry problems on quantum computers we a
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