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  • Hubbard 1D
    • Part 1: 1D Hubbard model
    • Part 2: Snake layout and fSWAP
    • Part 3: Qiskit and Fire Opal
    • Part 4: 120-qubit run
    • Part 5: Time-to-answer
    • Part 6: Tensor networks
    • Part 7: Majorana propagation
    • Part 8: Reading heatmaps
    • Part 9: Digital vs cold-atom labs
    • Part 10: Official Monoprop benchmark
  • Hubbard 2D
    • Part 1: 1D to 2D
    • Part 2: Cuprates
    • Part 3: 3×3
    • Part 4: Time
    • Part 5: 4×4
    • Part 6: 6×6 Fez
  • Hadron
    • Part 1: Hadron on a quantum processor
    • Part 2: Quarks and confinement
    • Part 3: SU(2) and LSH
    • Part 4: Hamiltonian and circuit
    • Part 5: Fire Opal
    • Part 6: Classical simulations
    • Part 7: Quantum advantage
  • Black Hole OLE
    • Part 1: What we ran
    • Part 2: How OLE works
    • Part 3: Fire Opal and Kingston
    • Part 4: The tensor-network challenge
    • Part 5: Hawking and scrambling
    • Part 6: What the result proves
    • Part 7: Local toy model
    • Part 8: QGSS26 compatibility
  • Random Graph
    • Start here
    • Part 1: Theory
    • Part 2: Circuit
    • Part 3: Qiskit
    • Part 4: Complexity
    • Part 5: Verification
    • Part 6: Workflow
    • Part 7: Conclusion
  • QOS QML
    • Tutorial: UMI counts to a four-qubit circuit
    • Part 1: The QML task
    • Part 2: QOS theory
    • Part 3: Gene expression to 40 qubits
    • Part 4: JAX to hardware
    • Part 5: Readout and classifier
    • Part 6: 40-qubit result
    • Part 7: Route to quantum advantage
    • Part 8: 60-qubit result
  • Floquet-Ising
    • Part 1: Floquet physics
    • Part 2: Ising cycle
    • Part 3: Two-qubit toy model
    • Part 4: Oscillation and entanglement
    • Part 5: Noise and error mitigation
    • Part 6: Toward 51 qubits
  • Work
    • Quantum Gold
      • Part 1: Why gold is a relativistic quantum problem
      • Part 2: Why the 2025 gold VQE study stalled
      • Part 3: From QE and spin–orbit coupling to Qiskit
      • Part 4: Twelve gold spinor modes on four qubits
      • Part 5: The 24-qubit route: an active window for transport
      • Part 6: 24 qubits on IBM and with Fire Opal
      • Part 7: The road to quantum advantage for gold
      • Part 8: 24 gold spinor modes on IBM with ZNE-PEA
    • HaPPY Gravity
      • Part 1: Gravity as a phase gate
      • Part 2: Bosons and convergence
      • Part 3: The dynamic HaPPY benchmark
      • Part 4: The N=145 classical audit
      • Part 5: MPS and Majorana baselines
      • Part 6: PEA/ZNE and the decisive test
    • Fibonacci Anyons
      • Part 1: Fusion and braiding
      • Part 2: The 3/5/9-qubit ladder
      • Part 3: Why nine qubits were too deep
      • Part 4: Structure-aware simplification
      • Part 5: IBM hardware diagnostic
      • Part 6: Results and open questions
  • Advantage List
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Fermi-Hubbard 2D cuprate series

This project follows a concrete 2D Fermi-Hubbard simulation route: from the earlier 1D IBM/TDVP validation series, through a cuprate-oriented square-lattice Hubbard model, to exact 3×3 validation, IBM and Fire Opal diagnostics, and tensor-network baselines up to the current 6×6 diagnostic step.

The claim boundary is practical and cautious. The current 2D results are diagnostic validation data. They are not a claim of d-wave superconductivity, not material evidence for cuprates, and not a quantum-advantage claim.

Article series

  1. Part 1: from 1D to 2D
  2. Part 2: 2D Hubbard, cuprates, and Google/Willow context
  3. Part 3: our 3×3 implementation
  4. Part 4: time evolution and hardware diagnostics
  5. Part 5: 4×4 hardware and tensor baselines
  6. Part 6: 6×6 tensor baseline, IBM diagnostics, and Fire Opal Fez

Project links

  • Project repository
  • First Fermi-Hubbard project page
  • Google/Willow 2D Fermi-Hubbard paper
  • Google/Willow dataset
  • Q-CTRL 1D Fermi-Hubbard paper

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