XVIth International Workshop on
Quantum Systems in
Chemistry and Physics
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Quantum Chemistry on Quantum Computers
L. Veis and J. Pittner
J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Prague, Czech Republic
Quantum computers are appealing for their ability to solve some tasks much faster than their classical counterparts, e.g. efficiently factore integers. Quantum chemistry could in principle benefit from them as well, for example by an efficient solution of many-body Hamiltonian eigenvalue problem [1]. As was shown in the seminal work by Aspuru-Guzik et. al. [2], quantum computers, if available, would be able to perform the full configuration interaction (FCI) energy calculations with only a polynomial scaling, in contrast to conventional computers where FCI scales exponentially.

We have developed a code for simulation of quantum computers and implemented our version of the quantum full configuration interaction (QFCI) method which uses the iterative phase estimation algorithm. This approach reduces demands on the total number of quantum bits (qubits) as only one is needed in the read-out part of the quantum register and the whole algorithm proceeds in an iterative manner.

We have tested its performance and applicability for non-relativistic as well as relativistic CI energy calculations. Non-relativistic QFCI calculations of the four lowest lying electronic states of methylene molecule (CH2), which exhibit a multireference character were performed [3]. It has been shown that with a suitably chosen initial state of the quantum register, one is able to achieve the probability amplification regime of the iterative phase estimation even for nearly dissociated molecule. Relativistic Kramers-restricted CI calculations employing the QFCI algorithm have been applied to the spin-orbit coupling in the SbH molecule [4]. We have also designed the quantum circuits for the simplest proof-of-principle physical realizations of relativistic quantum chemical computations on quantum computers.

[1] Abrams, D. S.; Lloyd, S. Phys.Rev.Lett. 1999, 83, 5162–5165.
[2] Aspuru-Guzik, A.; Dutoi, A. D.; Love, P. J.; Head-Gordon, M. Science 2005, 309, 1704–1707.
[3] Veis, L.; Pittner, J. J. Chem. Phys. 2010, 133, 194106.
[4] Veis, L; Višnák, J.; Fleig, T.; Knecht, S.; Saue, T.; Visscher, L.; Pittner, J. in preparation


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