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Hückel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated π-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over the direct mapping and allows for quantum simulation of the HMO model for systems with up to 2n conjugated centers with n qubits. The transformation of the Hückel Hamiltonian to qubit space is achieved by two different strategies: an iterative refinement transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated π-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. However, the higher excited states of large systems are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C60 fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are easily adaptable to similar problems of different complexity in other fields of research. [ABSTRACT FROM AUTHOR]

We elaborate the two-component Douglas-Kroll reduction of the Dirac-Kohn-Sham problem of relativistic density-functional theory as introduced by Matveev and Rösch [J. Chem. Phys. 118, 3997 (2003)]. That method retains corrections to the Coulomb self-interaction (or Hartree) term of the energy functional that are due to the picture change. Using analytic expressions for the matrix elements, one is able to abandon the resolution of the identity approach for a crucial step of the relativistic transformation. Thus, a major source of uncertainties of the method is eliminated because basis sets no longer have to be extended by functions of higher angular momentum, previously required to ensure kinetic balance. This approach also relies on the electron charge-density fitting scheme via an auxiliary basis set. An efficient approximate implementation results if one restricts the relativistic transformation to the spherically symmetric atom-centered auxiliary functions. It provides accurate results while simplifying greatly the expressions for the matrix elements of the relativistically transformed operators and significantly reducing the computational effort. We demonstrate the performance of the method for the fine structure of one-electron levels of the Hg atom, the g-tensor shifts of NO2, and the properties of the diatomic molecules Bi2, Pb2, PbO, and TlH. [ABSTRACT FROM AUTHOR]