The variational quantum eigensolver (VQE) with shallow or constant-depth quantum circuits is one of the most pursued approaches in the noisy intermediate-scale quantum (NISQ) devices with incoherent errors. In this study, the divide-and-conquer (DC) linear scaling technique, which divides the entire system into several fragments, is applied to the VQE algorithm based on the unitary coupled cluster (UCC) method, denoted as DC-qUCC/VQE, to reduce the number of required qubits. The unitarity of the UCC ansatz that enables the evaluation of the total energy as well as various molecular properties as expectation values can be easily implemented on quantum devices because the quantum gates are unitary operators themselves. Based on this feature, the present DC-qUCC/VQE algorithm is designed to conserve the total number of electrons in the entire system using the density matrix evaluated on a quantum computer. Numerical assessments clarified that the energy errors of the DC-qUCC/VQE calculations decrease by using the constraint of the total number of electrons. Furthermore, the DC-qUCC/VQE algorithm could reduce the number of quantum gates and shows the possibility of decreasing incoherent errors.

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In this study, we propose the quantum algorithm based on the unitary coupled cluster linear response theory for excited-state calculations with single and double excitations, denoted as qUCCSD-LR. Instead of the standard eigenvalue-problem-based scheme, the algorithm utilizes the dynamical-polarizability-based scheme, where the pole relative to the frequency of an external electric field corresponds to an excited state. Numerical applications of the qUCCSD-LR method to H2 could reproduce the dynamical polarizabilities, excitation energies and oscillator strengths obtained by the standard CCSD-LR method. Furthermore, potential energy curves for the double bond rotation in the ground and excited states of C2H4 were accurately calculated by the proposed method.