Simulating a ring-like Hubbard system with a quantum computer

TL;DR

This paper demonstrates how current quantum computers can simulate a four-site Hubbard ring, accurately locating phase transitions and calculating ground state energies using advanced variational algorithms and error mitigation techniques.

Contribution

It introduces a specialized variational ansatz leveraging symmetries and a Lanczos-inspired error mitigation for simulating quantum many-body systems on real quantum hardware.

Findings

Accurate ground state energies obtained on IBM quantum hardware.

Successful identification of phase transition in the Hubbard ring.

Benchmark results for near-term quantum simulation capabilities.

Abstract

We develop a workflow to use current quantum computing hardware for solving quantum many-body problems, using the example of the fermionic Hubbard model. Concretely, we study a four-site Hubbard ring that exhibits a transition from a product state to an intrinsically interacting ground state as hopping amplitudes are changed. We locate this transition and solve for the ground state energy with high quantitative accuracy using a variational quantum algorithm executed on an IBM quantum computer. Our results are enabled by a variational ansatz that takes full advantage of the maximal set of commuting $\mathbb{Z}_2$ symmetries of the problem and a Lanczos-inspired error mitigation algorithm. They are a benchmark on the way to exploiting near term quantum simulators for quantum many-body problems.