Perturbatively expanded sample-based quantum diagonalization for ground state energy calculation

The Selected Quantum Doubles (SQD) methods are among the most reliable approaches for quantum computation, capable of achieving high-accuracy simulations of electronic structure problems. Despite their strengths, SQD methods encounter challenges related to the selection of the initial state and the efficient management of extensive configuration spaces. This is particularly due to the presence of numerous configurations with low significance, which can limit scalability and accuracy. To address these issues, we have developed a perturbative quantum method capable of generating an initial state that is both accurate and flexible, alongside a procedure to manage the scalability of the method. Regarding the first objective, a parameterized Unitary Coupled Cluster Doubles (UCCD) approach has been developed, which generates a wavefunction comparable in quality to the Coupled Cluster Doubles (CCD) reference state. At this juncture, it is possible to augment this parameterized UCCD state to incorporate the principal single excited configurations. This augmentation step is essential to ensure that the initial state possesses sufficient flexibility to account for configurations that are combinations of single and double excited configurations. The second objective is the enhancement of the methodology's scalability. This objective is achieved by first identifying, through a perturbative approach, the most significant higher-order configurations. This allows for a smaller configurational CI Hamiltonian. Conversely, the second set of configurations will not be included in the Hamiltonian CI but will be evaluated solely within a perturbative framework using second-order perturbation theory (PT2). This combined approach leverages the strengths of both variational and perturbative methods, enabling the simulation to closely approximate Full Configuration Interaction (FCI) results while operating within a significantly reduced configurational space. This methodology resembles the most common Selected Configurations Interaction plus Perturbation methodology, while distinguishing itself through an improved selection process, which will be further refined in the future. The method will be tested on a highly correlated molecular system (linear chain of 8 Hydrogen) in minimal basis set. The molecule has been optimized in pyscf with MP2 method and def2-svp basis set.