Fully algebraic and self-consistent effective dynamics in a static quantum embedding

Reduced Density Matrix Sampling: Self-consistent Embedding and Multiscale Electronic Structure on Current Generation Quantum Computers

“…These approaches fall under the umbrella of quantum embedding or quantum cluster methods, and are amongst the most promising for QPU-enhanced materials modelling [21,72,73]. We investigate the recently-developed 'Energy-weighted Density Matrix Embedding Theory' (EwDMET) as a promising candidate in this direction [22][23][24].…”

“…In this case, it is more appropriate to consider the active quantum region in a real-space local picture, under the assumption that local quantum fluctuations dominate, such as those in the d-orbitals of a transition metal oxide material. This is the approach taken in various quantum embedding methods such as dynamical mean-field theory [21], and in this work we consider the related energyweighted density matrix embedding theory (EwDMET) [22][23][24]. We perform the self-consistency at the level of energy weighted density matrices, denoting the moments of the local density of states, resulting in a systematic expansion of the zero-temperature DMFT physics [24].…”

“…This is the approach taken in various quantum embedding methods such as dynamical mean-field theory [21], and in this work we consider the related energyweighted density matrix embedding theory (EwDMET) [22][23][24]. We perform the self-consistency at the level of energy weighted density matrices, denoting the moments of the local density of states, resulting in a systematic expansion of the zero-temperature DMFT physics [24]. For both of these approaches, we demonstrate the fidelity of the QPU sampling of the active space RDMs required for a fully QPU-coupled self-consistent algorithm, and consider the scaling of sampling operations as the active space increases in size in future applications.…”

On the pure state $v$-representability of density matrix embedding theory

“…5,36 , and for additional work, including some that goes beyond assuming a mean-field Φ, see Refs. 3,[24][25][26][27]29,[45][46][47][48][49] ). The correlation potential u is determined by a self-consistent matching procedure and this is the mathematical problem we seek to address.…”

“…In the context of SCF-DMET, the procedure for correlation potential fitting is a crucial step for numerical robustness and different approaches have been proposed 3,5,19,27,28,35,36,48,49 . One place where numerical issues can arise is when the global low-level Hamiltonian becomes gapless, in which case the least-squares cost function becomes non-differentiable.…”