add hubbard_openfermion

quantum_simulation_recipe/fermion.py

@@ -320,4 +320,59 @@ def LiH():
     LiH_fermion_hamiltonian = get_fermion_operator(LiH_molecular_hamiltonian)
     LiH_qubit_hamiltonian = jordan_wigner(LiH_fermion_hamiltonian)
     LiH_hamiltonian_list = openfermion_matrix_list(LiH_qubit_hamiltonian)
-    return LiH_hamiltonian_list
+    return LiH_hamiltonian_list
+
+
+
+"""Define the Hubbard Hamiltonian by OpenFermion."""
+class hubbard_openfermion:
+    def __init__(self, nsites, U, J=-1.0, pbc=False, verbose=False):
+        # Each site has two spins.
+        self.n_qubits = 2 * nsites
+
+        def fop_2_sparse(fops):
+            return [of.get_sparse_operator(fop, n_qubits=self.n_qubits).todense() for fop in fops ]
+
+        # One-body (hopping) terms.
+        self.one_body_fops = [op + of.hermitian_conjugated(op) for op in (
+                of.FermionOperator(((i, 1), (i + 2, 0)), coefficient=J) for i in range(self.n_qubits - 2))]
+        self.one_body_L = len(self.one_body_fops)
+        self.one_body_sparse = fop_2_sparse(self.one_body_fops)
+
+        # Two-body (charge-charge) terms.
+        self.two_body_fops = [
+            of.FermionOperator(((i, 1), (i, 0), (i + 1, 1), (i + 1, 0)), coefficient=U)
+            for i in range(0, self.n_qubits, 2)]
+        self.two_body_sparse = fop_2_sparse(self.two_body_fops)
+
+        self.h_fop = of.fermi_hubbard(1, nsites, tunneling=-J, coulomb=U, periodic=pbc)
+        self.h_sparse = of.get_sparse_operator(self.h_fop)
+        self.ground_energy, self.ground_state = of.get_ground_state(self.h_sparse)
+        assert sum(self.one_body_fops) + sum(self.two_body_fops) == self.h_fop
+        if verbose: 
+            print('one_body_terms: \n', self.one_body_fops)
+            print('one_body_L: ', self.one_body_L)
+            # print('one_body[0]: \n', self.one_body_sparse[0])
+            print('one_body[0]: \n', of.get_sparse_operator(self.one_body_fops[0]))
+            # print('sparse two-body: \n', of.get_sparse_operator(sum(self.two_body_fops)))
+            # print('sparse two-body[0]: \n', self.two_body_sparse[0])
+            # print('ground energy: \n', self.ground_energy)
+        # return ground_energy
+
+        self.one_body_01 = [term for index, term in enumerate(self.one_body_fops) if index % 4 == 0 or index % 4 == 1]
+        self.one_body_01_sparse = fop_2_sparse(self.one_body_01)
+        # print(self.one_body_01)
+        self.one_body_23 = [term for index, term in enumerate(self.one_body_fops) if index % 4 == 2 or index % 4 == 3]
+        self.one_body_23_sparse = fop_2_sparse(self.one_body_23)
+        # print(self.one_body_23)
+        assert sum(self.one_body_01) + sum(self.one_body_23) == sum(self.one_body_fops)
+
+        self.one_body_0 = [term for index, term in enumerate(self.one_body_fops) if index % 3 == 0]
+        self.one_body_1 = [term for index, term in enumerate(self.one_body_fops) if index % 3 == 1]
+        self.one_body_2 = [term for index, term in enumerate(self.one_body_fops) if index % 3 == 2]
+
+        assert sum(self.one_body_0) + sum(self.one_body_1)  + sum(self.one_body_2) == sum(self.one_body_fops)
+
+        self.one_body_0_sparse = [term for index, term in enumerate(self.one_body_sparse) if index % 3 == 0]
+        self.one_body_1_sparse = [term for index, term in enumerate(self.one_body_sparse) if index % 3 == 1]
+        self.one_body_2_sparse = [term for index, term in enumerate(self.one_body_sparse) if index % 3 == 2]

quantum_simulation_recipe/test.ipynb

@@ -144,6 +144,51 @@
     "plh.ham_xyz"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "dd5a2e4f",
+   "metadata": {},
+   "source": [
+    "### Fermi-Hubbard"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "e856807f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "one body terms:  [-1.0 [0^ 2] +\n",
+      "-1.0 [2^ 0], -1.0 [1^ 3] +\n",
+      "-1.0 [3^ 1], -1.0 [2^ 4] +\n",
+      "-1.0 [4^ 2], -1.0 [3^ 5] +\n",
+      "-1.0 [5^ 3], -1.0 [4^ 6] +\n",
+      "-1.0 [6^ 4], -1.0 [5^ 7] +\n",
+      "-1.0 [7^ 5]]\n",
+      "two body terms:  [1 [0^ 0 1^ 1], 1 [2^ 2 3^ 3], 1 [4^ 4 5^ 5], 1 [6^ 6 7^ 7]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "n = 4\n",
+    "# n = 5\n",
+    "r = 10000\n",
+    "epsilon = 1e-3\n",
+    "J, U = -1, 1\n",
+    "\n",
+    "t_num = 100\n",
+    "t_list = np.logspace(-1, 3, num=t_num)\n",
+    "# t_list = np.logspace(1.5, 3, num=t_num)\n",
+    "hubbard = hubbard_openfermion(n, U, verbose=False)\n",
+    "print('one body terms: ', hubbard.one_body_fops)\n",
+    "print('two body terms: ', hubbard.two_body_fops)\n",
+    "h_group = [sum(hubbard.one_body_01_sparse), sum(hubbard.one_body_23_sparse), sum(hubbard.two_body_sparse)]"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "d7fe9c22",
@@ -638,7 +683,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3.8.8 ('base')",
+   "display_name": "base",
    "language": "python",
    "name": "python3"
   },
@@ -653,11 +698,6 @@
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
    "version": "3.10.14"
-  },
-  "vscode": {
-   "interpreter": {
-    "hash": "4e8ef2f9fcac0817bca9a7ca376f64f20b4df5ea3bf7af756a50bda7d3557ea6"
-   }
   }
  },
  "nbformat": 4,