Unraveling correlated material properties with noisy quantum computers: Natural orbitalized variational quantum eigensolving of extended impurity models within a slave-boson approach

TL;DR

This paper introduces a hybrid quantum-classical method using a NISQ computer to solve extended impurity models in the Hubbard model, improving accuracy and efficiency through natural orbital transformation and a novel ansatz, enabling better space-resolved correlation property calculations.

Contribution

It presents the NOization method with a new MREP ansatz for solving two-impurity models on NISQ devices, extending previous local approaches and enhancing accuracy and scalability.

Findings

Achieved accurate quasiparticle weights and self-energies in noisy conditions.

Demonstrated faster and more accurate variational optimization with natural orbital basis.

Enabled larger embedded problems to be tackled with current quantum hardware.

Abstract

We propose a method for computing space-resolved correlation properties of the two-dimensional Hubbard model within a quantum-classical embedding strategy that uses a Noisy, Intermediate Scale Quantum (NISQ) computer to solve the embedded model. While previous approaches were limited to purely local, one-impurity embedded models, requiring at most four qubits and relatively shallow circuits, we solve a two-impurity model requiring eight qubits with an advanced hybrid scheme on top of the Variational Quantum Eigensolver algorithm. This iterative scheme, dubbed Natural Orbitalization (NOization), gradually transforms the single-particle basis to the approximate Natural-Orbital basis, in which the ground state can be minimally expressed, at the cost of measuring the one-particle reduced density-matrix of the embedded problem. We show that this transformation tends to make the variational optimization of existing (but too deep) ansatz circuits faster and more accurate, and we propose an ansatz, the Multireference Excitation Preserving (MREP) ansatz, that achieves great expressivity without requiring a prohibitive gate count. The one-impurity version of the ansatz has only one parameter, making the ground state preparation a trivial step, which supports the optimal character of our approach. Within a Rotationally Invariant Slave Boson embedding scheme that requires a minimal number of bath sites and does not require computing the full Green's function, the NOization combined with the MREP ansatz allow us to compute accurate, space-resolved quasiparticle weights and static self-energies for the Hubbard model even in the presence of noise levels representative of current NISQ processors. This paves the way to a controlled solution of the Hubbard model with larger and larger embedded problems solved by quantum computers.