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haiqu.sdk.skqd.hubbard_hamiltonian(norb, t, U, periodic=False)

Build 1D Fermi-Hubbard Hamiltonian tensors in site basis. 
H = -t * sum_{<i,j>,sigma} (c^dag_i c_j + h.c.) + U * sum_i n_up_i n_down_i
  • Parameters:
    • norb (int) — Number of spatial orbitals (lattice sites). Must be >= 2.
    • t (float) — Hopping parameter (kinetic energy).
    • U (float) — On-site interaction strength (potential energy).
    • periodic (bool) — Whether to use periodic boundary conditions.
  • Returns: (h1e, h2e) — one-body tensor shape (norb, norb) and two-body tensor shape (norb, norb, norb, norb).
  • Return type: tuple[ndarray, ndarray]

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haiqu.sdk.skqd.build_hubbard_site_basis_krylov_circuits(norb, krylov_dim, dt, h1e, h2e)

Build Krylov subspace circuits for the Hubbard model in site basis. Generates {|psi0>, e^{-iHdt}|psi0>, e^{-2iHdt}|psi0>, ...} where |psi0> is the antiferromagnetic Neel state and time evolution uses a second-order Trotter decomposition with CPhase gates on all orbitals.
  • Parameters:
    • norb (int) — Number of spatial orbitals.
    • krylov_dim (int) — Dimension of the Krylov subspace (number of time-evolution steps + 1).
    • dt (float) — Time step for Trotter evolution.
    • h1e (ndarray) — One-body Hamiltonian tensor, shape (norb, norb).
    • h2e (ndarray) — Two-body Hamiltonian tensor, shape (norb, norb, norb, norb).
  • Returns: List of quantum circuits representing the Krylov subspace.
  • Return type: list[QuantumCircuit]