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

TL;DR

This paper demonstrates that self-consistent multiscale quantum-classical algorithms can be effectively implemented on current quantum computers, enabling accurate electronic structure calculations and property sampling despite hardware noise.

Contribution

It introduces a robust, self-consistent embedding approach using reduced density matrices on current quantum hardware, with error mitigation and basis optimization for improved accuracy.

Findings

Self-consistent algorithms are robust against quantum hardware noise.

Reliable sampling of non-energetic properties like dipole moments achieved.

Uncertainties from iterative optimization are smaller than energy variances.

Abstract

We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum chemistry and condensed matter physics. In both of these contexts, a strongly correlated quantum region of the extended system is isolated and self-consistently coupled to its environment via the sampling of reduced density matrices. We analyze the viability of current generation quantum devices to provide the required fidelity of these objects for a robust and efficient optimization of this subspace. We show that with a simple error mitigation strategy and optimization of compact tensor product bases to minimize the number of terms to sample, these self-consistent algorithms are indeed highly robust, even in the presence of significant noises on quantum hardware. Furthermore, we demonstrate the use of these density matrices for the sampling of non-energetic properties, including dipole moments and Fermi liquid parameters in condensed phase systems, achieving a reliable accuracy with sparse sampling. It appears that uncertainties derived from the iterative optimization of these subspaces is smaller than variances in the energy for a single subspace optimization with current quantum hardware. This boosts the prospect for routine self-consistency to improve the choice of correlated subspaces in hybrid quantum-classical approaches to electronic structure for large systems in this multiscale fashion.