Simulating a ring-like Hubbard system with a quantum computer

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.

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• A Hybrid Quantum-Classical Method for Electron-Phonon Systems
• Quantum simulation costs for Suzuki-Trotter decomposition of quantum many-body lattice models
• Optimization strategies in WAHTOR algorithm for quantum computing empirical ansatz: a comparative study
• Recursive relations and quantum eigensolver algorithms within modified Schrieffer--Wolff transformations for the Hubbard dimer