Krylov variational quantum algorithm for first principles materials simulations

TL;DR

This paper introduces a quantum algorithm combining Krylov subspace methods with variational techniques to efficiently compute Green's functions for materials, demonstrated on a strongly correlated insulator using quantum emulation.

Contribution

It presents a novel Krylov variational quantum algorithm integrated with DMFT for first principles material simulations, suitable for near-term quantum hardware.

Findings

Successfully predicted insulating properties of La$_{2}$CuO$_4$ with 8 qubits

Demonstrated potential for quantum advantage in materials simulations

Applicable to strongly correlated materials on near-term quantum devices

Abstract

We propose an algorithm to obtain Green's functions as a continued fraction on quantum computers, which is based on the construction of the Krylov basis using variational quantum algorithms, and included in a Lanczos iterative scheme. This allows the integration of quantum algorithms with first principles material science simulations, as we demonstrate within the dynamical mean-field theory (DMFT) framework. DMFT enables quantitative predictions for strongly correlated materials, and relies on the calculation of Green's functions. On conventional computers the exponential growth of the Hilbert space with the number of orbitals limits DMFT to small systems. Quantum computers open new avenues and can lead to a significant speedup in the computation of expectation values required to obtain the Green's function. We apply our Krylov variational quantum algorithm combined with DMFT to the charge transfer insulator La$_{2}$CuO$_4$ using a quantum computing emulator, and show that with 8 qubits it predicts the correct insulating material properties for the paramagnetic phase. We therefore expect that the method is ideally suited to perform simulations for real materials on near term quantum hardware.