Dynamical Self-energy Mapping (DSEM) for Creation of Sparse Hamiltonians Suitable for Quantum Computing.

Area of Science:

• Computational Chemistry
• Quantum Computing

Background:

• Accurate molecular simulations are crucial for understanding chemical processes.
• Full Hamiltonian representations in quantum computing can be computationally expensive, limiting problem size and circuit depth.

Purpose of the Study:

• To introduce a novel two-step procedure, Dynamical Self-Energy Mapping (DSEM), for generating sparse Hamiltonian representations of molecular systems.
• To demonstrate the efficiency and accuracy of DSEM for calculating molecular energies.
• To explore DSEM's potential as a hybrid classical-quantum algorithm for quantum computing.

Main Methods:

• DSEM involves a two-step process: first, evaluating the molecular system's self-energy using a low-level method, and second, finding a sparse Hamiltonian that approximates this self-energy.
• A high-level method then refines the dynamical self-energy using the sparse Hamiltonian for subsequent calculations.
• The sparse Hamiltonian contains O(n^2) terms, where n is the number of orbitals.

Main Results:

• Tests on small molecular systems show that sparse Hamiltonian parameterizations yield highly accurate total energies.
• The DSEM method successfully generates sparse Hamiltonians that effectively represent molecular systems.
• The resulting sparse Hamiltonians significantly reduce the number of terms compared to full Hamiltonians.

Conclusions:

• DSEM provides a computationally efficient pathway to obtain accurate molecular energies.
• The sparse Hamiltonians generated by DSEM can reduce quantum circuit depth by an order of magnitude, making quantum simulations more feasible.
• DSEM is a promising technique for hybrid classical-quantum algorithms in quantum chemistry.