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 manybody Hamiltonian eigenvalue problem [1]. As was shown in the seminal work by AspuruGuzik 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 readout part of the quantum register and the whole algorithm proceeds in an iterative manner.
We have tested its performance and applicability for nonrelativistic as well as relativistic CI energy calculations. Nonrelativistic QFCI calculations of the four lowest lying electronic states of methylene molecule (CH_{2}), 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 Kramersrestricted CI calculations employing the QFCI algorithm have been applied to the spinorbit coupling in the SbH molecule [4]. We have also designed the quantum circuits for the simplest proofofprinciple physical realizations of relativistic quantum chemical computations on quantum computers.
[1] Abrams, D. S.; Lloyd, S. Phys.Rev.Lett. 1999, 83, 5162–5165.
[2] AspuruGuzik, A.; Dutoi, A. D.; Love, P. J.; HeadGordon, 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
