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Researchers used a variational quantum algorithm to simulate the Fermi-Hubbard model, observing key features like metal-insulator transitions and antiferromagnetic order on a quantum processor.

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Area of Science:

  • Quantum computing
  • Condensed matter physics
  • Computational chemistry

Background:

  • The Fermi-Hubbard model is crucial for understanding strongly-correlated electronic systems but remains computationally challenging.
  • Near-term quantum hardware may struggle to represent large Fermi-Hubbard model instances accurately.

Purpose of the Study:

  • To experimentally demonstrate that a low-depth variational quantum algorithm can capture essential characteristics of the Fermi-Hubbard model.
  • To explore medium-size instances of the Fermi-Hubbard model beyond classically solvable 1D cases.

Main Methods:

  • Implementation of a variational quantum algorithm on a superconducting quantum processor using 16 qubits.
  • Simulation of 1x8 and 2x4 instances of the Fermi-Hubbard model.
  • Application of error mitigation techniques, including model symmetries and a specialized fermionic simulation method.
  • Introduction of a novel variational optimization algorithm utilizing iterative Bayesian updates.

Main Results:

  • Successful reproduction of qualitative features of medium-size Fermi-Hubbard model instances.
  • Observation of the metal-insulator transition and Friedel oscillations in 1D simulations.
  • Detection of antiferromagnetic order in both 1D and 2D simulations.
  • Demonstration of scalability beyond 1D Fermi-Hubbard instances.

Conclusions:

  • A low-depth variational quantum algorithm is effective for simulating key aspects of the Fermi-Hubbard model on current quantum hardware.
  • The experimental results align with theoretical predictions for ground-state properties.
  • The developed methods offer a pathway for tackling larger and more complex quantum systems.