Quantum chemical calculations are one of the most intensively investigated applications of quantum computers. To use quantum computers for practical research tools in quantum chemistry, it is necessary to develop new techniques to efficiently treat molecular systems having complicated electronic structures such as open shell molecules carrying unpaired electrons. Most of quantum algorithms for quantum chemical calculations reported so far assume that the Hartree-Fock wave function is a good approximation of the ground state wave function, but such assumption cannot be validated for open shell low-spin states carrying spin-beta unpaired electrons. This is because the wave functions of open shell low-spin states are described by the linear combination of many Slater determinants to satisfy the symmetry requirement of the spin operator S2. The square overlap between the full-CI and the wave function approximated by single Slater determinant decreases exponentially against the number of unpaired electrons and those of spin-beta. To treat open shell electronic structures efficiently on quantum computers, we have to develop new theoretical methods to prepare sophisticated approximate wave functions for open shell molecules and to determine the spin quantum number of arbitrary wave functions. Here, we propose quantum circuits for the preparation of spin symmetry-adapted approximate wave functions suitable for the initial guess wave functions of open shell molecules [1-3] and a quantum algorithm to compute the eigenvalue of the S2 operator by using the quantum phase estimation technique [4].

Toward quantum chemical calculations of open shell molecules on quantum computers

Macromolecular Chemistry: The Second Century

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ACS Spring 2020 National Meeting & Expo

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