Towards Studying Superconductivity in the Fermi-Hubbard Model on Rydberg Atoms

TL;DR

This paper introduces a quantum sampling method using Rydberg atoms to approximate the ground state energy of the Fermi-Hubbard model, demonstrating advantages over random sampling and potential for studying superconductivity.

Contribution

It develops a sample-based quantum diagonalization approach leveraging Rydberg atom processors and explores its effectiveness for large-scale Fermi-Hubbard models.

Findings

Heisenberg model sampling converges near the ground state for up to 56 qubits

Rydberg atom sampling outperforms random sampling even with fewer samples

The method provides a basis for studying superconductivity in quantum systems

Abstract

We present a method for calculating the ground state energy of the Fermi-Hubbard model leveraging Rydberg atom processors and sample-based quantum diagonalization (SQD). By exploiting the perturbative relationship between the Fermi-Hubbard and Heisenberg models, the procedure samples from the Heisenberg model as prepared on the Rydberg atom processor, and uses the samples to diagonalize the Fermi-Hubbard model for large U. We include anisotropy and next-nearest-neighbor interactions and discuss the relevant regime for quasi-superconductivity in the 1-dimensional Fermi- Hubbard model. Numerical and experimental results on the Aquila quantum processor are presented for ground state energy calculations as well as the chemical potential. We find that the Heisenberg model sampling in the studied regime is sufficient to converge near to the ground state for up to 56 qubits, and we see a clear advantage of Rydberg atom sampling as opposed to random sampling even with 10x more samples for diagonalization. We also present a gate-based implementation of the gate-based SQD algorithm on IBM Quantum hardware for 56-qubit Hubbard model as a benchmark. Finally, we provide a gap analysis for studying emergent superconductivity using this method.