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

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 4 qubits and relatively shallow circuits, we solve a two-impurity model requiring 8 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 oneparticle 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 Multi-Reference Excitation Preserving (MREP) ansatz, that achieves great expressivity without requiring a prohibitive gate count, thus bridging the gap between hardware-efficient and physically-motivated strategies in variational ansatz design. 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.

The Weak, the Strong and the Long Correlation Regimes of the Two-Dimensional Hubbard Model at Finite Temperature

“…While the Hubbard model has mainly been the subject of theoretical studies, it can now also be directly simulated at moderately-high temperatures by means of cold atoms trapped in optical lattices [16][17][18][19][20][21][22]. More recently, efforts in quantum computing technology have been aimed at the Hubbard model with the hope of finding effective algorithms for noisy near-term quantum hardware [23][24][25][26][27][28]. Large collaborative projects have been formed with the aim of comparing the results of numerous state-of-the-art algorithms in order to better understand the model as well as provide unbiased consensus benchmarks for future experimental and theoretical studies [29][30][31][32].…”