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<p>Solving the Fermi–Hubbard model is a central task in the study of strongly correlated materials. Digital quantum computers can, in principle, be suitable for this purpose, but have so far been limited to quasi-one-dimensional models. This is because of exponential overheads caused by the interplay of noise and the non-locality of the mapping between fermions and qubits. Here we use a trapped-ion quantum computer to experimentally demonstrate that a recently developed local encoding can overcome this problem. In particular, we show that suitable reordering of terms and application of circuit identities—a scheme called corner hopping—substantially reduces the cost of simulating fermionic hopping. This enables the efficient preparation of the ground state of a 6 × 6 spinless Fermi–Hubbard model encoded in 48 physical qubits. We also develop two error mitigation schemes for systems with conserved quantities, based on local postselection and on extrapolation of local observables, respectively. Our results suggest that Fermi–Hubbard models beyond classical simulability can be addressed by digital quantum computers without large increases in gate fidelity.</p>

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Experimental demonstration of breakeven for a compact fermionic encoding

  • 期刊论文

  • 发表日期：

    2025年6月16日

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  • Ramil Nigmatullin,
  • Kévin Hémery,
  • Khaldoon Ghanem,
  • Steven Moses,
  • Dan Gresh,
  • Peter Siegfried,
  • Michael Mills,
  • Thomas Gatterman,
  • Nathan Hewitt,
  • Etienne Granet,
  • Henrik Dreyer

摘要

Solving the Fermi–Hubbard model is a central task in the study of strongly correlated materials. Digital quantum computers can, in principle, be suitable for this purpose, but have so far been limited to quasi-one-dimensional models. This is because of exponential overheads caused by the interplay of noise and the non-locality of the mapping between fermions and qubits. Here we use a trapped-ion quantum computer to experimentally demonstrate that a recently developed local encoding can overcome this problem. In particular, we show that suitable reordering of terms and application of circuit identities—a scheme called corner hopping—substantially reduces the cost of simulating fermionic hopping. This enables the efficient preparation of the ground state of a 6 × 6 spinless Fermi–Hubbard model encoded in 48 physical qubits. We also develop two error mitigation schemes for systems with conserved quantities, based on local postselection and on extrapolation of local observables, respectively. Our results suggest that Fermi–Hubbard models beyond classical simulability can be addressed by digital quantum computers without large increases in gate fidelity.