FermionOperator({
- (cre_a(0), des_a(3)): 0.5,
+ (cre_b(1), des_b(5), cre_a(4)): 1+1j,
(cre_a(3), des_a(0)): -0.25,
- (cre_b(1), des_b(5), cre_a(4)): 1+1j
+ (cre_a(0), des_a(3)): 0.5
})
FermionOperator({
- (cre_b(1), des_b(5), cre_a(4)): 2+2j,
(cre_a(3), des_a(0)): -0.5,
+ (cre_b(1), des_b(5), cre_a(4)): 2+2j,
(cre_a(0), des_a(3)): 1
})
FermionOperator({
(cre_b(2)): 0+1j,
- (des_a(3), des_b(3)): -0.25,
- (cre_a(0), des_a(3)): 0.5,
(cre_a(3), des_a(0)): -0.25,
- (cre_b(1), des_b(5), cre_a(4)): 1+1j
+ (cre_b(1), des_b(5), cre_a(4)): 1+1j,
+ (cre_a(0), des_a(3)): 0.5,
+ (des_a(3), des_b(3)): -0.25
})
FermionOperator({
- (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,
- (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,
(cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,
- (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,
+ (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,
(cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,
- (cre_a(3), des_a(0), cre_b(2)): 0-0.25j
+ (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,
+ (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,
+ (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625
})
ffsim is a software library for simulating fermionic quantum circuits that preserve particle number +
ffsim is a software library for simulating fermionic quantum circuits that conserve particle number and the Z component of spin. This category includes many quantum circuits used for quantum chemistry simulations. By exploiting the symmetries and using specialized algorithms, ffsim can simulate these circuits much faster than a generic quantum circuit simulator.
diff --git a/searchindex.js b/searchindex.js index 5883e6416..385943532 100644 --- a/searchindex.js +++ b/searchindex.js @@ -1 +1 @@ -Search.setIndex({"docnames": ["api/ffsim", "api/ffsim.contract", "api/ffsim.linalg", "api/ffsim.random", "api/ffsim.testing", "index", "tutorials/01-introduction", "tutorials/02-orbital-rotation", "tutorials/03-double-factorized", "tutorials/04-lucj", "tutorials/05-entanglement-forging", "tutorials/06-fermion-operator"], "filenames": ["api/ffsim.rst", "api/ffsim.contract.rst", "api/ffsim.linalg.rst", "api/ffsim.random.rst", "api/ffsim.testing.rst", "index.rst", "tutorials/01-introduction.ipynb", "tutorials/02-orbital-rotation.ipynb", "tutorials/03-double-factorized.ipynb", "tutorials/04-lucj.ipynb", "tutorials/05-entanglement-forging.ipynb", "tutorials/06-fermion-operator.ipynb"], "titles": ["ffsim", "ffsim.contract", "ffsim.linalg", "ffsim.random", "ffsim.testing", "Welcome to ffsim\u2019s documentation!", "Introduction to ffsim", "Orbital rotations and quadratic Hamiltonians", "Diagonal Coulomb operators and double-factorized Trotter simulation", "The local unitary cluster Jastrow (LUCJ) ansatz", "Entanglement forging", "The FermionOperator class"], "terms": {"i": [0, 1, 2, 3, 5, 6, 7, 8, 9, 11], "softwar": [0, 5, 6], "librari": [0, 5, 6], "fast": 0, "simul": [0, 5, 6, 7, 9, 10], "fermion": [0, 5, 6, 7, 9, 11], "quantum": [0, 5, 6, 8, 9], "circuit": [0, 5, 6], "class": [0, 3, 5, 6, 9], "doublefactorizedhamiltonian": [0, 5, 8], "one_body_tensor": [0, 7, 8], "diag_coulomb_mat": [0, 8], "orbital_rot": [0, 1, 6, 7, 8], "constant": [0, 8, 9], "0": [0, 7, 8, 9, 10, 11], "z_represent": [0, 1], "fals": [0, 1, 2, 9, 10, 11], "sourc": [0, 1, 2, 3, 4], "base": [0, 2, 9, 10], "object": [0, 2, 9, 11], "A": [0, 1, 2, 3, 4, 7, 8, 9, 11], "hamiltonian": [0, 5, 9, 10], "doubl": [0, 2, 5, 9], "factor": [0, 2, 5, 9], "form": [0, 1, 2, 7, 8, 9, 11], "low": [0, 2, 6], "rank": [0, 2, 3], "decomposit": [0, 2], "The": [0, 1, 2, 3, 4, 5, 6, 7, 8], 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(ffsim.doublefactorizedhamiltonian attribute)": [[0, "ffsim.DoubleFactorizedHamiltonian.orbital_rotations"]], "orbital_rotations (ffsim.ucjoperator attribute)": [[0, "ffsim.UCJOperator.orbital_rotations"]], "orbital_symmetries (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.orbital_symmetries"]], "simulate_qdrift_double_factorized() (in module ffsim)": [[0, "ffsim.simulate_qdrift_double_factorized"]], "simulate_trotter_double_factorized() (in module ffsim)": [[0, "ffsim.simulate_trotter_double_factorized"]], "slater_determinant() (in module ffsim)": [[0, "ffsim.slater_determinant"]], "slater_determinant_one_rdm() (in module ffsim)": [[0, "ffsim.slater_determinant_one_rdm"]], "spin (ffsim.fermionaction attribute)": [[0, "ffsim.FermionAction.spin"]], "to_number_representation() (ffsim.doublefactorizedhamiltonian method)": [[0, "ffsim.DoubleFactorizedHamiltonian.to_number_representation"]], "to_parameters() (ffsim.ucjoperator method)": [[0, "ffsim.UCJOperator.to_parameters"]], "to_t_amplitudes() (ffsim.ucjoperator method)": [[0, "ffsim.UCJOperator.to_t_amplitudes"]], "to_z_representation() (ffsim.doublefactorizedhamiltonian method)": [[0, "ffsim.DoubleFactorizedHamiltonian.to_z_representation"]], "trace() (in module ffsim)": [[0, "ffsim.trace"]], "two_body_tensor (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.two_body_tensor"]], "two_body_tensor (ffsim.molecularhamiltonian attribute)": [[0, "ffsim.MolecularHamiltonian.two_body_tensor"]], "z_representation (ffsim.doublefactorizedhamiltonian attribute)": [[0, "ffsim.DoubleFactorizedHamiltonian.z_representation"]], "contract_diag_coulomb() (in module ffsim.contract)": [[1, "ffsim.contract.contract_diag_coulomb"]], "contract_num_op_sum() (in module ffsim.contract)": [[1, "ffsim.contract.contract_num_op_sum"]], "diag_coulomb_linop() (in module ffsim.contract)": [[1, "ffsim.contract.diag_coulomb_linop"]], "ffsim.contract": [[1, "module-ffsim.contract"]], "num_op_sum_linop() (in module ffsim.contract)": [[1, "ffsim.contract.num_op_sum_linop"]], "one_body_linop() (in module ffsim.contract)": [[1, "ffsim.contract.one_body_linop"]], "apply_matrix_to_slices() (in module ffsim.linalg)": [[2, "ffsim.linalg.apply_matrix_to_slices"]], "double_factorized() (in module ffsim.linalg)": [[2, "ffsim.linalg.double_factorized"]], "double_factorized_t2() (in module ffsim.linalg)": [[2, "ffsim.linalg.double_factorized_t2"]], "expm_multiply_taylor() (in module ffsim.linalg)": [[2, "ffsim.linalg.expm_multiply_taylor"]], "ffsim.linalg": [[2, "module-ffsim.linalg"]], "givens_decomposition() (in module ffsim.linalg)": [[2, "ffsim.linalg.givens_decomposition"]], "is_antihermitian() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_antihermitian"]], "is_hermitian() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_hermitian"]], "is_orthogonal() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_orthogonal"]], "is_real_symmetric() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_real_symmetric"]], "is_special_orthogonal() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_special_orthogonal"]], "is_unitary() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_unitary"]], "lup() (in module ffsim.linalg)": [[2, "ffsim.linalg.lup"]], "modified_cholesky() (in module ffsim.linalg)": [[2, "ffsim.linalg.modified_cholesky"]], "reduced_matrix() (in module ffsim.linalg)": [[2, "ffsim.linalg.reduced_matrix"]], "ffsim.random": [[3, "module-ffsim.random"]], "random_antihermitian() (in module ffsim.random)": [[3, "ffsim.random.random_antihermitian"]], "random_hermitian() (in module ffsim.random)": [[3, "ffsim.random.random_hermitian"]], "random_orthogonal() (in module ffsim.random)": [[3, "ffsim.random.random_orthogonal"]], "random_real_symmetric_matrix() (in module ffsim.random)": [[3, "ffsim.random.random_real_symmetric_matrix"]], "random_special_orthogonal() (in module ffsim.random)": [[3, "ffsim.random.random_special_orthogonal"]], "random_statevector() (in module ffsim.random)": [[3, "ffsim.random.random_statevector"]], "random_t2_amplitudes() (in module ffsim.random)": [[3, "ffsim.random.random_t2_amplitudes"]], "random_two_body_tensor_real() (in module ffsim.random)": [[3, "ffsim.random.random_two_body_tensor_real"]], "random_unitary() (in module ffsim.random)": [[3, "ffsim.random.random_unitary"]], "ffsim.testing": [[4, "module-ffsim.testing"]], "random_nelec() (in module ffsim.testing)": [[4, "ffsim.testing.random_nelec"]], "random_occupied_orbitals() (in module ffsim.testing)": [[4, "ffsim.testing.random_occupied_orbitals"]]}}) \ No newline at end of file diff --git a/tutorials/01-introduction.ipynb b/tutorials/01-introduction.ipynb index d5ba19349..3797ae9e6 100644 --- a/tutorials/01-introduction.ipynb +++ b/tutorials/01-introduction.ipynb @@ -16,10 +16,10 @@ "execution_count": 1, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:10:56.876770Z", - "iopub.status.busy": "2023-10-27T02:10:56.876313Z", - "iopub.status.idle": "2023-10-27T02:10:57.234710Z", - "shell.execute_reply": "2023-10-27T02:10:57.233997Z" + "iopub.execute_input": "2023-10-27T03:04:57.255539Z", + "iopub.status.busy": "2023-10-27T03:04:57.255034Z", + "iopub.status.idle": "2023-10-27T03:04:57.653213Z", + "shell.execute_reply": "2023-10-27T03:04:57.652569Z" } }, "outputs": [], @@ -62,10 +62,10 @@ "execution_count": 2, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:10:57.238646Z", - "iopub.status.busy": "2023-10-27T02:10:57.238253Z", - "iopub.status.idle": "2023-10-27T02:10:57.243775Z", - "shell.execute_reply": "2023-10-27T02:10:57.243164Z" + "iopub.execute_input": "2023-10-27T03:04:57.657905Z", + "iopub.status.busy": "2023-10-27T03:04:57.656590Z", + "iopub.status.idle": "2023-10-27T03:04:57.662682Z", + "shell.execute_reply": "2023-10-27T03:04:57.662136Z" } }, "outputs": [], @@ -93,10 +93,10 @@ "execution_count": 3, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:10:57.246706Z", - "iopub.status.busy": "2023-10-27T02:10:57.246424Z", - "iopub.status.idle": "2023-10-27T02:10:57.250646Z", - "shell.execute_reply": "2023-10-27T02:10:57.250044Z" + "iopub.execute_input": "2023-10-27T03:04:57.667736Z", + "iopub.status.busy": "2023-10-27T03:04:57.666400Z", + "iopub.status.idle": "2023-10-27T03:04:57.671189Z", + "shell.execute_reply": "2023-10-27T03:04:57.670658Z" } }, "outputs": [], diff --git a/tutorials/02-orbital-rotation.ipynb b/tutorials/02-orbital-rotation.ipynb index f9f1f6346..7699c0f29 100644 --- a/tutorials/02-orbital-rotation.ipynb +++ b/tutorials/02-orbital-rotation.ipynb @@ -43,10 +43,10 @@ "execution_count": 1, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:10:58.972368Z", - "iopub.status.busy": "2023-10-27T02:10:58.971701Z", - "iopub.status.idle": "2023-10-27T02:10:59.327235Z", - "shell.execute_reply": "2023-10-27T02:10:59.326526Z" + "iopub.execute_input": "2023-10-27T03:04:59.630059Z", + "iopub.status.busy": "2023-10-27T03:04:59.629560Z", + "iopub.status.idle": "2023-10-27T03:05:00.024476Z", + "shell.execute_reply": "2023-10-27T03:05:00.023597Z" } }, "outputs": [], @@ -111,10 +111,10 @@ "execution_count": 2, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:10:59.331910Z", - "iopub.status.busy": "2023-10-27T02:10:59.331556Z", - "iopub.status.idle": "2023-10-27T02:10:59.363811Z", - "shell.execute_reply": "2023-10-27T02:10:59.363117Z" + "iopub.execute_input": "2023-10-27T03:05:00.028824Z", + "iopub.status.busy": "2023-10-27T03:05:00.028106Z", + "iopub.status.idle": "2023-10-27T03:05:00.061962Z", + "shell.execute_reply": "2023-10-27T03:05:00.061268Z" } }, "outputs": [], @@ -158,10 +158,10 @@ "execution_count": 3, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:10:59.367924Z", - "iopub.status.busy": "2023-10-27T02:10:59.367666Z", - "iopub.status.idle": "2023-10-27T02:10:59.380003Z", - "shell.execute_reply": "2023-10-27T02:10:59.379403Z" + "iopub.execute_input": "2023-10-27T03:05:00.067442Z", + "iopub.status.busy": "2023-10-27T03:05:00.066016Z", + "iopub.status.idle": "2023-10-27T03:05:00.079662Z", + "shell.execute_reply": "2023-10-27T03:05:00.079034Z" } }, "outputs": [], @@ -201,10 +201,10 @@ "execution_count": 4, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:10:59.383243Z", - "iopub.status.busy": "2023-10-27T02:10:59.382787Z", - "iopub.status.idle": "2023-10-27T02:10:59.387977Z", - "shell.execute_reply": "2023-10-27T02:10:59.387405Z" + "iopub.execute_input": "2023-10-27T03:05:00.084489Z", + "iopub.status.busy": "2023-10-27T03:05:00.083296Z", + "iopub.status.idle": "2023-10-27T03:05:00.090411Z", + "shell.execute_reply": "2023-10-27T03:05:00.089817Z" } }, "outputs": [], diff --git a/tutorials/03-double-factorized.ipynb b/tutorials/03-double-factorized.ipynb index 793d55de6..c061160c4 100644 --- a/tutorials/03-double-factorized.ipynb +++ b/tutorials/03-double-factorized.ipynb @@ -43,10 +43,10 @@ "execution_count": 1, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:11:01.239526Z", - "iopub.status.busy": "2023-10-27T02:11:01.239298Z", - "iopub.status.idle": "2023-10-27T02:11:01.672486Z", - "shell.execute_reply": "2023-10-27T02:11:01.671867Z" + "iopub.execute_input": "2023-10-27T03:05:01.960181Z", + "iopub.status.busy": "2023-10-27T03:05:01.959717Z", + "iopub.status.idle": "2023-10-27T03:05:02.404039Z", + "shell.execute_reply": "2023-10-27T03:05:02.403342Z" } }, "outputs": [ @@ -92,10 +92,10 @@ "execution_count": 2, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:11:01.676217Z", - "iopub.status.busy": "2023-10-27T02:11:01.675393Z", - "iopub.status.idle": "2023-10-27T02:11:01.682498Z", - "shell.execute_reply": "2023-10-27T02:11:01.681935Z" + "iopub.execute_input": "2023-10-27T03:05:02.408011Z", + "iopub.status.busy": "2023-10-27T03:05:02.407295Z", + "iopub.status.idle": "2023-10-27T03:05:02.417935Z", + "shell.execute_reply": "2023-10-27T03:05:02.417313Z" } }, "outputs": [ @@ -226,10 +226,10 @@ "execution_count": 3, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:11:01.685379Z", - "iopub.status.busy": "2023-10-27T02:11:01.684954Z", - "iopub.status.idle": "2023-10-27T02:11:01.690254Z", - "shell.execute_reply": "2023-10-27T02:11:01.689707Z" + "iopub.execute_input": "2023-10-27T03:05:02.423483Z", + "iopub.status.busy": "2023-10-27T03:05:02.421763Z", + "iopub.status.idle": "2023-10-27T03:05:02.431334Z", + "shell.execute_reply": "2023-10-27T03:05:02.430699Z" } }, "outputs": [], @@ -284,10 +284,10 @@ "execution_count": 4, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:11:01.693242Z", - "iopub.status.busy": "2023-10-27T02:11:01.692815Z", - "iopub.status.idle": "2023-10-27T02:11:01.697021Z", - "shell.execute_reply": "2023-10-27T02:11:01.696463Z" + "iopub.execute_input": "2023-10-27T03:05:02.434936Z", + "iopub.status.busy": "2023-10-27T03:05:02.434685Z", + "iopub.status.idle": "2023-10-27T03:05:02.439093Z", + "shell.execute_reply": "2023-10-27T03:05:02.438396Z" } }, "outputs": [], @@ -324,10 +324,10 @@ "execution_count": 5, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:11:01.798461Z", - "iopub.status.busy": "2023-10-27T02:11:01.797539Z", - "iopub.status.idle": "2023-10-27T02:11:01.804011Z", - "shell.execute_reply": "2023-10-27T02:11:01.803354Z" + "iopub.execute_input": "2023-10-27T03:05:02.559009Z", + "iopub.status.busy": "2023-10-27T03:05:02.558102Z", + "iopub.status.idle": "2023-10-27T03:05:02.564371Z", + "shell.execute_reply": "2023-10-27T03:05:02.563761Z" } }, "outputs": [ @@ -363,10 +363,10 @@ "execution_count": 6, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:11:01.807404Z", - "iopub.status.busy": "2023-10-27T02:11:01.806733Z", - "iopub.status.idle": "2023-10-27T02:11:01.818517Z", - "shell.execute_reply": "2023-10-27T02:11:01.817866Z" + "iopub.execute_input": "2023-10-27T03:05:02.567736Z", + "iopub.status.busy": "2023-10-27T03:05:02.567083Z", + "iopub.status.idle": "2023-10-27T03:05:02.584110Z", + "shell.execute_reply": "2023-10-27T03:05:02.583071Z" } }, "outputs": [ @@ -405,10 +405,10 @@ "execution_count": 7, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:11:01.821521Z", - "iopub.status.busy": "2023-10-27T02:11:01.821296Z", - "iopub.status.idle": "2023-10-27T02:11:01.831674Z", - "shell.execute_reply": "2023-10-27T02:11:01.831110Z" + "iopub.execute_input": "2023-10-27T03:05:02.587264Z", + "iopub.status.busy": "2023-10-27T03:05:02.586808Z", + "iopub.status.idle": "2023-10-27T03:05:02.600814Z", + "shell.execute_reply": "2023-10-27T03:05:02.599564Z" } }, "outputs": [ @@ -446,10 +446,10 @@ "execution_count": 8, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:11:01.835578Z", - "iopub.status.busy": "2023-10-27T02:11:01.835146Z", - "iopub.status.idle": "2023-10-27T02:11:01.879635Z", - "shell.execute_reply": "2023-10-27T02:11:01.878876Z" + "iopub.execute_input": "2023-10-27T03:05:02.604427Z", + "iopub.status.busy": "2023-10-27T03:05:02.603969Z", + "iopub.status.idle": "2023-10-27T03:05:02.648867Z", + "shell.execute_reply": "2023-10-27T03:05:02.648260Z" } }, "outputs": [ @@ -457,14 +457,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Fidelity of Trotter-evolved state with exact state: 0.9999906233109686" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n" + "Fidelity of Trotter-evolved state with exact state: 0.9999906233109686\n" ] } ], @@ -496,10 +489,10 @@ "execution_count": 9, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:11:01.882831Z", - "iopub.status.busy": "2023-10-27T02:11:01.882543Z", - "iopub.status.idle": "2023-10-27T02:11:01.913639Z", - "shell.execute_reply": "2023-10-27T02:11:01.913025Z" + "iopub.execute_input": "2023-10-27T03:05:02.654063Z", + "iopub.status.busy": "2023-10-27T03:05:02.652939Z", + "iopub.status.idle": "2023-10-27T03:05:02.679846Z", + "shell.execute_reply": "2023-10-27T03:05:02.679254Z" } }, "outputs": [ @@ -538,10 +531,10 @@ "execution_count": 10, "metadata": { "execution": { - "iopub.execute_input": "2023-10-27T02:11:01.916639Z", - "iopub.status.busy": "2023-10-27T02:11:01.916394Z", - "iopub.status.idle": "2023-10-27T02:11:01.932237Z", - "shell.execute_reply": "2023-10-27T02:11:01.931529Z" + "iopub.execute_input": "2023-10-27T03:05:02.684588Z", + "iopub.status.busy": "2023-10-27T03:05:02.683495Z", + "iopub.status.idle": "2023-10-27T03:05:02.697257Z", + "shell.execute_reply": "2023-10-27T03:05:02.696649Z" } }, "outputs": [ diff --git a/tutorials/04-lucj.html b/tutorials/04-lucj.html index 398083bbb..63957239b 100644 --- a/tutorials/04-lucj.html +++ b/tutorials/04-lucj.html @@ -95,8 +95,8 @@
-converged SCF energy = -77.4456267643961
-CASCI E = -77.6290254326717 E(CI) = -3.57322412553863 S^2 = 0.0000000
+converged SCF energy = -77.4456267643962
+CASCI E = -77.6290254326717 E(CI) = -3.57322412553862 S^2 = 0.0000000
-E(CCSD) = -77.49387212754469 E_corr = -0.0482453631485175
-Energy at initialialization: -77.46975600021719
+E(CCSD) = -77.49387212754471 E_corr = -0.04824536314851448
+Energy at initialialization: -77.46975600021672
To facilitate variational optimization of the ansatz, UCJOperator implements methods for conversion to and from a vector of real-valued parameters. The precise relation between a parameter vector and the matrices of the UCJ operator is somewhat complicated. In short, the parameter vector stores the entries of the UCJ matrices in a non-redundant way (for the orbital rotations, the parameter vector actually stores the entries of their generators.)
-Energy at initialialization: -75.6836617444762
+Energy at initialialization: -75.68366174447618
FermionOperator({
(cre_a(3), des_a(0)): -0.25,
- (cre_b(1), des_b(5), cre_a(4)): 1+1j,
- (cre_a(0), des_a(3)): 0.5
+ (cre_a(0), des_a(3)): 0.5,
+ (cre_b(1), des_b(5), cre_a(4)): 1+1j
})
@@ -99,7 +99,7 @@
-'FermionOperator({((True, False, 3), (False, False, 0)): -0.25+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 0), (False, False, 3)): 0.5+0j})'
+'FermionOperator({((True, False, 3), (False, False, 0)): -0.25+0j, ((True, False, 0), (False, False, 3)): 0.5+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j})'
FermionOperators support arithmetic operations. Note that when multiplying a FermionOperator by a scalar, the scalar must go on the left, i.e. 2 * op and not op * 2.
FermionOperator({
(cre_a(3), des_a(0), cre_b(2)): 0-0.25j,
- (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,
- (des_a(3), des_b(3)): 0.0625,
- (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,
- (cre_b(1), des_b(5), cre_a(4)): 2+2j,
+ (cre_b(2)): 0-0.25j,
(cre_a(3), des_a(0)): -0.5,
- (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,
- (cre_a(0), des_a(3)): 1,
(cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,
- (cre_b(2)): 0-0.25j,
- (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625
+ (cre_a(0), des_a(3)): 1,
+ (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,
+ (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,
+ (des_a(3), des_b(3)): 0.0625,
+ (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,
+ (cre_b(1), des_b(5), cre_a(4)): 2+2j,
+ (cre_a(0), des_a(3), cre_b(2)): 0+0.5j
})
@@ -163,16 +163,16 @@
FermionOperator({
(cre_a(3), des_a(0), cre_b(2)): -1,
- (cre_a(0), des_a(3), cre_b(2)): 2,
- (des_a(3), des_b(3)): 0-1.25j,
- (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,
- (cre_b(1), des_b(5), cre_a(4)): 12-12j,
+ (cre_b(2)): -5,
(cre_a(3), des_a(0)): 0+3j,
- (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,
- (cre_a(0), des_a(3)): 0-6j,
(cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,
- (cre_b(2)): -5,
- (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j
+ (cre_a(0), des_a(3)): 0-6j,
+ (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,
+ (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,
+ (des_a(3), des_b(3)): 0-1.25j,
+ (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,
+ (cre_b(1), des_b(5), cre_a(4)): 12-12j,
+ (cre_a(0), des_a(3), cre_b(2)): 2
})
@@ -193,16 +193,16 @@
FermionOperator({
- (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,
- (cre_b(2)): -5,
- (cre_b(1), cre_a(4), des_b(5)): -12+12j,
- (cre_a(3), des_a(0)): 0+3j,
- (cre_b(2), cre_a(0), des_a(3)): 2,
(des_b(3), des_a(3)): 0+1.25j,
+ (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,
(cre_b(2), cre_a(3), des_a(0)): -1,
(cre_a(0), des_a(3)): 0-6j,
(cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j,
- (cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j
+ (cre_b(2), cre_a(0), des_a(3)): 2,
+ (cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,
+ (cre_b(2)): -5,
+ (cre_b(1), cre_a(4), des_b(5)): -12+12j,
+ (cre_a(3), des_a(0)): 0+3j
})
-array([0. +0.j , 0. +0.j ,
- 0. +0.j , 0. +0.j ,
- 0.09345703-0.26351017j, 0. +0.j ,
- 0. +0.j , 0. +0.j ,
- 0. +0.j ])
+array([ 0. +0.j , 0. +0.j ,
+ 0. +0.j , 0. +0.j ,
+ -0.04860684-0.04058205j, 0. +0.j ,
+ 0. +0.j , 0. +0.j ,
+ 0. +0.j ])
It can also be passed into most linear algebra routines in scipy.sparse.linalg.