Quantum Monte Carlo formulation of the second order algebraic diagrammatic construction: Toward a massively parallel correlated excited state method

The quantum Monte Carlo (QMC) algebraic diagrammatic construction (ADC) method is introduced, which solves the eigenvalue problem of the second-order ADC scheme for the polarization propagator stochastically within the framework of QMC methodology allowing for massively parallel computations. As common virtue of the Monte Carlo integration techniques, quantum Monte Carlo algebraic diagrammatic construction (QMCADC) enables exploitation of the sparsity of the effective ADC matrix, and it reduces the memory requirements by storing only a portion of configurations at each iteration. Furthermore, distributing memory and processing loads to different computing nodes enables the use of fast developing parallel computing resources. Here, the theory and implementation of QMCADC is reported and its viability is demonstrated by the first proof-of-principle calculations. The focus lies on the first excited state and the reproduction of the corresponding lowest vertical excitation energy of various molecular systems. QMCADC is shown to be a genuine stochastic solution of the ADC eigenvalue problem, and exact ADC values can be obtained with a marginal controllable error.