Dynamical Self-energy Mapping (DSEM) for quantum computing

Understand

For noisy intermediate-scale quantum (NISQ) devices only a moderate number of qubits with a limited coherence is available thus enabling only shallow circuits and a few time evolution steps in the currently performed quantum computations.

• Here, we present how to bypass this challenge in practical molecular chemistry simulations on NISQ devices by employing a classical-quantum hybrid algorithm allowing us to produce a sparse Hamiltonian which contains only $\mathcal{O}(n^2)$ terms in a Gaussian orbital basis when compared to the $\mathcal{O}(n^4)$ terms of a standard Hamiltonian, where $n$ is the number of orbitals in the system.
• Classical part of this hybrid entails parameterization of the sparse, fictitious Hamiltonian in such a way that it recovers the self-energy of the original molecular system.
• Quantum machine then uses this fictitious Hamiltonian to calculate the self-energy of the system.