Module: openfermion

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OpenFermion

For more information, examples, or tutorials visit our website:

www.openfermion.org

Modules

chem module

circuits module

config module

contextuality module: tests for whether operators are contextual contextuality

contrib module

functionals module

hamiltonians module

linalg module

measurements module

ops module: This module should contain objects that describe the algebra of various operators and representations which can be thought of as abstract instances that serve as storage of the operators.

testing module

transforms module

utils module

Classes

class AsymmetricSplitOperatorTrotterStep: A method for performing a Trotter step.

class BinaryCode: The BinaryCode class provides a representation of an encoding-decoding pair for binary vectors of different lengths, where the decoding is allowed to be non-linear.

class BinaryCodeError: Common base class for all non-exit exceptions.

class BinaryPolynomial: The BinaryPolynomial class provides an analytic representation of non-linear binary functions.

class BinaryPolynomialError: Common base class for all non-exit exceptions.

class BosonOperator: BosonOperator stores a sum of products of bosonic ladder operators.

class ControlledAsymmetricSplitOperatorTrotterStep: A method for performing a Trotter step.

class ControlledSymmetricSplitOperatorTrotterStep: A method for performing a Trotter step.

class CubicFermionicSimulationGate: w0|110⟩⟨101| + w1|110⟩⟨011| + w2|101⟩⟨011| + h.c. interaction.

class DOCIHamiltonian: Class for storing DOCI hamiltonians which are defined to be restrictions of fermionic operators to doubly occupied configurations.

class Davidson: Davidson algorithm to get the n states with smallest eigenvalues.

class DavidsonError: Exceptions.

class DavidsonOptions: Davidson algorithm iteration options.

class DiagonalCoulombHamiltonian: Class for storing Hamiltonians of the form

class DoubleExcitationGate: Evolve under -|0011⟩⟨1100| + h.c. for some time.

class EqualsTester: Tests equality against user-provided disjoint equivalence groups.

class FSwapPowGate: The FSWAP gate, possibly raised to a power.

class FenwickNode: Fenwick Tree node.

class FenwickTree: Recursive implementation of the Fenwick tree.

class FermiHubbardModel: A general, parameterized Fermi-Hubbard model.

class FermionOperator: FermionOperator stores a sum of products of fermionic ladder operators.

class Grid: A multi-dimension grid of points with an assigned length scale.

class HartreeFockFunctional: Implementation of the objective function code for Restricted Hartree-Fock

class HubbardLattice: Base class for a Hubbard model lattice.

class HubbardSquareLattice: A square lattice for a Hubbard model.

class InteractionOperator: Class for storing 'interaction operators' which are defined to be fermionic operators consisting of one-body and two-body terms which conserve particle number and spin.

class InteractionOperatorError: Common base class for all non-exit exceptions.

class InteractionOperatorFermionicGate: The Jordan-Wigner transform of \(\exp(-i H)\) for a fermionic Hamiltonian \(H\), where \(H\) is an interaction operator.

class InteractionRDM: Class for storing 1- and 2-body reduced density matrices.

class InteractionRDMError: Common base class for all non-exit exceptions.

class IsingOperator: The IsingOperator class provides an analytic representation of an Ising-type Hamiltonian, i.e.

class LinearQubitOperator: A LinearOperator implied from a QubitOperator.

class LinearQubitOperatorOptions: Options for LinearQubitOperator.

class LinearSwapNetworkTrotterAlgorithm: A Trotter algorithm using the "fermionic simulation gate".

class LowRankTrotterAlgorithm: A Trotter algorithm using the low rank decomposition strategy.

class MajoranaOperator: A linear combination of products of Majorana operators.

class MolecularData: Class for storing molecule data from a fixed basis set at a fixed geometry that is obtained from classical electronic structure packages.

class OperatorSpecificationError: Common base class for all non-exit exceptions.

class OperatorUtilsError: Common base class for all non-exit exceptions.

class ParallelLinearQubitOperator: A LinearOperator from a QubitOperator with multiple processors.

class ParityPreservingFermionicGate: The Jordan-Wigner transform of \(\exp(-i H)\) for a fermionic Hamiltonian \(H\).

class PhaseFitEstimator: A VPE estimator that works by fitting a set of known frequencies.

class PolynomialTensor: Class for storing tensor representations of operators that correspond with multilinear polynomials in the fermionic ladder operators.

class PolynomialTensorError: Common base class for all non-exit exceptions.

class QuadOperator: QuadOperator stores a sum of products of canonical quadrature operators.

class QuadraticFermionicSimulationGate: (w0 |10⟩⟨01| + h.c.) + w1 |11⟩⟨11| interaction.

class QuadraticHamiltonian: Class for storing Hamiltonians that are quadratic in the fermionic ladder operators.

class QuadraticHamiltonianError: Common base class for all non-exit exceptions.

class QuarticFermionicSimulationGate: Rotates Hamming-weight 2 states into their bitwise complements.

class QubitDavidson: Davidson algorithm applied to a QubitOperator.

class QubitOperator: A sum of terms acting on qubits, e.g., 0.5 * 'X0 X5' + 0.3 * 'Z1 Z2'.

class SparseDavidson: Davidson algorithm for a sparse matrix.

class Spin: An enumeration.

class SpinPairs: The spin orbitals corresponding to a pair of spatial orbitals.

class SplitOperatorTrotterAlgorithm: A Trotter algorithm using a split-operator approach.

class SplitOperatorTrotterStep: A method for performing a Trotter step.

class StabilizerError: Stabilizer error class.

class SymbolicOperator: Base class for FermionOperator and QubitOperator.

class SymmetricSplitOperatorTrotterStep: A method for performing a Trotter step.

class TrotterAlgorithm: An algorithm for performing a Trotter step.

class TrotterStep: A method for performing a Trotter step.

Functions

CRxxyy(...): Controlled version of openfermion.Rxxyy

CRyxxy(...): Controlled version of openfermion.Ryxxy

DoubleExcitation(...): Evolve under -|0011⟩⟨1100| + h.c. for some time.

FSWAP(...): The FSWAP gate, possibly raised to a power.

Rxxyy(...): Returns a gate with the matrix exp(-i rads (X⊗X + Y⊗Y) / 2).

Ryxxy(...): Returns a gate with the matrix exp(-i rads (Y⊗X - X⊗Y) / 2).

Rzz(...): Returns a gate with the matrix exp(-i Z⊗Z rads).

amplitude_damping_channel(...): Apply an amplitude damping channel

angstroms_to_bohr(...)

anticommutator(...): Compute the anticommutator of two operators.

antisymmetric_canonical_form(...): Compute the canonical form of an antisymmetric matrix.

append_random_vectors(...): Appends exactly col orthonormal random vectors for vectors.

apply_constraints(...): Function to use linear programming to apply constraints.

assert_equivalent_repr(...): Checks that eval(repr(v)) == v.

assert_implements_consistent_protocols(...): Checks that a value is internally consistent and has a good repr.

bch_expand(...): Compute log[e^{x_1} ... e^{x_N}] using the BCH formula.

binary_code_transform(...): Transforms a Hamiltonian written in fermionic basis into a Hamiltonian written in qubit basis, via a binary code.

binary_partition_iterator(...): Generator for a list of 2-partitions of N qubits such that all pairs of qubits are split in at least one partition, This follows a variation on ArXiv:1908.0562 - instead of explicitly partitioning the list based on the binary indices of the qubits, we repeatedly divide the list in two and then zip it back together.

bit_mask_of_modes_acted_on_by_fermionic_terms(...): Create a mask of which modes of the system are acted on by which terms.

bogoliubov_transform(...): Perform a Bogoliubov transformation.

bohr_to_angstroms(...)

bose_hubbard(...): Return symbolic representation of a Bose-Hubbard Hamiltonian.

boson_ladder_sparse(...): Make a matrix representation of a singular bosonic ladder operator in the Fock space.

boson_operator_sparse(...): Initialize a Scipy sparse matrix in the Fock space from a bosonic operator.

bravyi_kitaev(...): Apply the Bravyi-Kitaev transform.

bravyi_kitaev_code(...): The Bravyi-Kitaev transform as binary code.

bravyi_kitaev_fast(...): Find the Pauli-representation of InteractionOperator for Bravyi-Kitaev Super fast (BKSF) algorithm.

bravyi_kitaev_fast_edge_matrix(...): Use InteractionOperator to construct edge matrix required for the algorithm

bravyi_kitaev_fast_interaction_op(...): Transform from InteractionOperator to QubitOperator for Bravyi-Kitaev fast algorithm.

bravyi_kitaev_tree(...): Apply the "tree" Bravyi-Kitaev transform.

check_commuting_stabilizers(...): Auxiliary function checking that stabilizers commute.

check_no_sympy(...): Checks whether a SymbolicOperator contains any sympy expressions, which will prevent it being converted to a PolynomialTensor or DiagonalCoulombHamiltonian

check_stabilizer_linearity(...): Auxiliary function checking that stabilizers are linearly independent.

checksum_code(...): Checksum code for either even or odd Hamming weight.

chemist_ordered(...): Puts a two-body fermion operator in chemist ordering.

commutator(...): Compute the commutator of two operators.

constraint_matrix(...): Function to generate matrix of constraints.

count_qubits(...): Compute the minimum number of qubits on which operator acts.

dephasing_channel(...): Apply a dephasing channel

depolarizing_channel(...): Apply a depolarizing channel

diagonal_coulomb_potential_and_kinetic_terms_as_arrays(...): Give the potential and kinetic terms of a diagonal Coulomb Hamiltonian as arrays.

double_commutator(...): Return the double commutator [op1, [op2, op3]].

double_decoding(...): Concatenates two decodings

double_givens_rotate(...): Apply a double Givens rotation.

down_index(...): Function to return down-orbital index given a spatial orbital index.

dual_basis_external_potential(...): Return the external potential in the dual basis of arXiv:1706.00023.

dual_basis_jellium_model(...): Return jellium Hamiltonian in the dual basis of arXiv:1706.00023

dual_basis_kinetic(...): Return the kinetic operator in the dual basis of arXiv:1706.00023.

dual_basis_potential(...): Return the potential operator in the dual basis of arXiv:1706.00023

eigenspectrum(...): Compute the eigenspectrum of an operator.

erpa_eom_hamiltonian(...): Evaluate sum{a,b,c,d}h{a, b, d, c}

error_bound(...): Numerically upper bound the error in the ground state energy for the second order Trotter-Suzuki expansion.

error_operator(...): Determine the difference between the exact generator of unitary evolution and the approximate generator given by Trotter-Suzuki to the given order.

expectation(...): Compute the expectation value of an operator with a state.

expectation_computational_basis_state(...): Compute expectation value of operator with a state.

expectation_db_operator_with_pw_basis_state(...): Compute expectation value of a dual basis operator with a plane wave computational basis state.

expectation_one_body_db_operator_computational_basis_state(...): Compute expectation value of a 1-body dual-basis operator with a plane wave computational basis state.

expectation_three_body_db_operator_computational_basis_state(...): Compute expectation value of a 3-body dual-basis operator with a plane wave computational basis state.

expectation_two_body_db_operator_computational_basis_state(...): Compute expectation value of a 2-body dual-basis operator with a plane wave computational basis state.

fermi_hubbard(...): Return symbolic representation of a Fermi-Hubbard Hamiltonian.

fermionic_gaussian_decomposition(...): Decompose a matrix into a sequence of Givens rotations and particle-hole transformations on the last fermionic mode.

fermionic_simulation_gates_from_interaction_operator(...): Given \(H = \sum_{I \subset [n]} H_I\), returns gates \(\left\{G_I\right\} = \left\{e^{i H_I\right\}\).

fermionic_swap_trotter_error_operator_diagonal_two_body(...): Compute the fermionic swap network Trotter error of a diagonal two-body Hamiltonian.

ffft(...): Performs fast fermionic Fourier transform.

fit_known_frequencies(...): Fits a set of known exponential components to a dataset

fix_single_term(...): Auxiliary function for term reductions.

fixed_trace_positive_projection(...): Perform the positive projection with fixed trace

fourier_transform(...): Apply Fourier transform to change hamiltonian in plane wave basis.

freeze_orbitals(...): Fix some orbitals to be occupied and others unoccupied.

gaussian_state_preparation_circuit(...): Obtain the description of a circuit which prepares a fermionic Gaussian state.

general_basis_change(...): Change the basis of a general interaction tensor.

generate_hamiltonian(...)

generate_linear_qubit_operator(...): Generates a LinearOperator from a QubitOperator.

generate_parity_permutations(...): Generates the permutations and sign of a sequence by constructing a tree where the nth level contains all n-permutations of m (n < m) objects.

generate_random_vectors(...): Generates orthonormal random vectors with col columns.

geometry_from_file(...): Function to create molecular geometry from text file.

geometry_from_pubchem(...): Function to extract geometry using the molecule's name from the PubChem database.

get_boson_operator(...): Convert to BosonOperator.

get_chemist_two_body_coefficients(...): Convert two-body operator coefficients to low rank tensor.

get_density_matrix(...)

get_diagonal_coulomb_hamiltonian(...): Convert a FermionOperator to a DiagonalCoulombHamiltonian.

get_fermion_operator(...): Convert to FermionOperator.

get_file_path(...): Compute file_path for the file that stores operator.

get_gap(...): Compute gap between lowest eigenvalue and first excited state.

get_ground_state(...): Compute lowest eigenvalue and eigenstate.

get_interaction_operator(...): Convert a 2-body fermionic operator to InteractionOperator.

get_interaction_rdm(...): Build an InteractionRDM from measured qubit operators.

get_linear_qubit_operator_diagonal(...): Return a linear operator's diagonal elements.

get_majorana_operator(...): Convert to MajoranaOperator.

get_matrix_of_eigs(...): Transform the eigenvalues into a matrix corresponding to summing the adjoint rep.

get_molecular_data(...): Output a MolecularData object generated from an InteractionOperator

get_number_preserving_sparse_operator(...): Initialize a Scipy sparse matrix in a specific symmetry sector.

get_one_norm_int(...): Returns the 1-Norm of a RHF or ROHF Hamiltonian described in https://arxiv.org/abs/2103.14753 after a fermion-to-qubit transformation given nuclear constant, one-body (2D np.array) and two-body (4D np.array) integrals in spatial orbital basis.

get_one_norm_int_woconst(...): Returns 1-norm, emitting the constant term in the qubit Hamiltonian.

get_one_norm_mol(...): Returns the 1-Norm of a RHF or ROHF Hamiltonian described in https://arxiv.org/abs/2103.14753 after a fermion-to-qubit transformation given a MolecularData class.

get_one_norm_mol_woconst(...): Returns 1-norm, emitting the constant term in the qubit Hamiltonian.

get_phase_function(...): Generates an estimate of the phase function g(t) from circuit output

get_quad_operator(...): Convert to QuadOperator.

get_quadratic_hamiltonian(...): Convert a quadratic fermionic operator to QuadraticHamiltonian.

get_sparse_operator(...): Map an operator to a sparse matrix.

givens_decomposition(...): Decompose a matrix into a sequence of Givens rotations.

givens_decomposition_square(...): Decompose a square matrix into a sequence of Givens rotations.

givens_matrix_elements(...): Compute the matrix elements of the Givens rotation that zeroes out one of two row entries.

givens_rotate(...): Apply a Givens rotation to coordinates i and j of an operator.

group_into_tensor_product_basis_sets(...): Split an operator (instance of QubitOperator) into sub-operator QubitOperators, where each sub-operator has terms that are diagonal in the same tensor product basis.

haar_random_vector(...): Generate an n dimensional Haar randomd vector.

hartree_fock_state_jellium(...): Give the Hartree-Fock state of jellium.

heaviside(...): Heaviside function Theta(x - bias)

hermitian_conjugated(...): Return Hermitian conjugate of operator.

higham_polynomial(...): Calculate the higham_polynomial

higham_root(...): Find the root of f(sigma) = sum{j}Theta(l{i} - sigma)(l_{i} - sigma) = T

hypercube_grid_with_given_wigner_seitz_radius_and_filling(...): Return a Grid with the same number of orbitals along each dimension with the specified Wigner-Seitz radius.

inner_product(...): Compute inner product of two states.

interaction_operator(...)

interleaved_code(...): Linear code that reorders orbitals from even-odd to up-then-down.

inverse_fourier_transform(...): Apply inverse Fourier transform to change hamiltonian in plane wave dual basis.

is_hermitian(...): Test if operator is Hermitian.

is_identity(...): Check whether QubitOperator of FermionOperator is identity.

jellium_model(...): Return jellium Hamiltonian as FermionOperator class.

jordan_wigner(...): Apply the Jordan-Wigner transform to a FermionOperator, InteractionOperator, or DiagonalCoulombHamiltonian to convert to a QubitOperator.

jordan_wigner_code(...): The Jordan-Wigner transform as binary code.

jordan_wigner_dual_basis_hamiltonian(...): Return the dual basis Hamiltonian as QubitOperator.

jordan_wigner_dual_basis_jellium(...): Return the jellium Hamiltonian as QubitOperator in the dual basis.

jordan_wigner_ladder_sparse(...): Make a matrix representation of a fermion ladder operator.

jordan_wigner_one_body(...): Map the term a^\dagger_p a_q + h.c. to QubitOperator.

jordan_wigner_sparse(...): Initialize a Scipy sparse matrix from a FermionOperator.

jordan_wigner_two_body(...): Map the term a^\dagger_p a^\dagger_q a_r a_s + h.c. to QubitOperator.

jw_configuration_state(...): Function to produce a basis state in the occupation number basis.

jw_get_gaussian_state(...): Compute an eigenvalue and eigenstate of a quadratic Hamiltonian.

jw_get_ground_state_at_particle_number(...): Compute ground energy and state at a specified particle number.

jw_hartree_fock_state(...): Function to produce Hartree-Fock state in JW representation.

jw_number_indices(...): Return the indices for n_electrons in n_qubits under JW encoding

jw_number_restrict_operator(...): Restrict a Jordan-Wigner encoded operator to a given particle number

jw_number_restrict_state(...): Restrict a Jordan-Wigner encoded state to a given particle number

jw_slater_determinant(...): Obtain a Slater determinant.

jw_sparse_givens_rotation(...): Return the matrix (acting on a full wavefunction) that performs a Givens rotation of modes i and j in the Jordan-Wigner encoding.

jw_sparse_particle_hole_transformation_last_mode(...): Return the matrix (acting on a full wavefunction) that performs a particle-hole transformation on the last mode in the Jordan-Wigner encoding.

jw_sz_indices(...): Return the indices of basis vectors with fixed Sz under JW encoding.

jw_sz_restrict_operator(...): Restrict a Jordan-Wigner encoded operator to a given Sz value

jw_sz_restrict_state(...): Restrict a Jordan-Wigner encoded state to a given Sz value

kronecker_delta(...)

kronecker_operators(...): Return the Kronecker product of multiple sparse.csc_matrix operators.

lambda_norm(...): Computes the lambda norm relevant to LCU algorithms.

linearize_decoder(...): Outputs linear decoding function from input matrix

linearize_term(...): Function to return integer index of term indices.

load_molecular_hamiltonian(...): Attempt to load a molecular Hamiltonian with the given properties.

load_operator(...): Load FermionOperator or QubitOperator from file.

low_depth_second_order_trotter_error_bound(...): Numerically upper bound the error in the ground state energy for the second-order Trotter-Suzuki expansion.

low_depth_second_order_trotter_error_operator(...): Determine the difference between the exact generator of unitary evolution and the approximate generator given by the second-order Trotter-Suzuki expansion.

low_rank_two_body_decomposition(...): Convert two-body operator into sum of squared one-body operators.

majorana_operator(...): Initialize a Majorana operator.

make_atom(...): Prepare a molecular data instance for a single element.

make_atomic_lattice(...): Function to create atomic lattice with n_atoms.

make_atomic_ring(...): Function to create atomic rings with n_atoms.

make_reduced_hamiltonian(...): Construct the reduced Hamiltonian.

map_one_hole_dm_to_one_pdm(...): Convert a 1-hole-RDM to a 1-RDM

map_one_pdm_to_one_hole_dm(...): Convert a 1-RDM to a 1-hole-RDM

map_particle_hole_dm_to_one_pdm(...): Map the particle-hole-RDM to the 1-RDM

map_particle_hole_dm_to_two_pdm(...): Map the 2-RDM to the particle-hole-RDM

map_to_matrix(...)

map_to_tensor(...)

map_two_hole_dm_to_one_hole_dm(...): Map from 2-hole-RDM to 1-hole-RDM

map_two_hole_dm_to_two_pdm(...): Map from the 2-hole-RDM to the 2-RDM

map_two_pdm_to_one_pdm(...): Contract a 2-RDM to a 1-RDM

map_two_pdm_to_particle_hole_dm(...): Map the 2-RDM to the particle-hole-RDM

map_two_pdm_to_two_hole_dm(...): Map from the 2-RDM to the 2-hole-RDM

mccoy(...): Implement the McCoy formula on two operators of the form op_a^m op_b^n.

mean_field_dwave(...): Return symbolic representation of a BCS mean-field d-wave Hamiltonian.

module_importable(...): Without importing it, returns whether python module is importable.

name_molecule(...): Function to name molecules.

normal_ordered(...): Compute and return the normal ordered form of a FermionOperator, BosonOperator, QuadOperator, or InteractionOperator.

normal_ordered_ladder_term(...): Return a normal ordered FermionOperator or BosonOperator corresponding to single term.

normal_ordered_quad_term(...): Return a normal ordered QuadOperator corresponding to single term.

number_difference_operator(...)

number_operator(...): Return a fermionic or bosonic number operator.

one_body_fermion_constraints(...): Generates one-body positivity constraints on fermionic RDMs.

operator_to_vector(...): Function to map operator to vector.

optimal_givens_decomposition(...): Implement a circuit that provides the unitary that is generated by single-particle fermion generators

orthonormalize(...): Orthonormalize vectors, so that they're all normalized and orthogoal.

pair_between(...): Pairs between two fragments of a larger list

pair_within(...): Generates pairings of labels that contain each pair at least once.

pair_within_simultaneously(...): Generates simultaneous pairings between four-element combinations

pair_within_simultaneously_binned(...): Generates symmetry-respecting pairings between four-elements in a list

pair_within_simultaneously_symmetric(...): Generates symmetry-respecting pairings between four-elements in a list

parity_code(...): The parity transform (arXiv:1208.5986) as binary code.

partition_iterator(...): Generator for a list of k-partitions of N qubits such that all sets of k qubits are perfectly split in at least one partition, following ArXiv:1908.05628

pauli_exp_to_qasm(...): Exponentiate a list of QubitOperators to a QASM string generator.

pauli_string_iterator(...): Generates a set of Pauli strings such that each word of k Pauli operators lies in at least one string.

plane_wave_external_potential(...): Return the external potential operator in plane wave basis.

plane_wave_hamiltonian(...): Returns Hamiltonian as FermionOperator class.

plane_wave_kinetic(...): Return the kinetic energy operator in the plane wave basis.

plane_wave_potential(...): Return the e-e potential operator in the plane wave basis.

prepare_gaussian_state(...): Prepare a fermionic Gaussian state from a computational basis state.

prepare_one_body_squared_evolution(...): Get Givens angles and DiagonalHamiltonian to simulate squared one-body.

prepare_slater_determinant(...): Prepare a Slater determinant from a computational basis state.

preprocess_lcu_coefficients_for_reversible_sampling(...): Prepares data used to perform efficient reversible roulette selection.

project_onto_sector(...): Remove qubit by projecting onto sector.

projection_error(...): Calculate the error from the project_onto_sector function.

prony(...): Estimates amplitudes and phases of a sparse signal using Prony's method.

prune_unused_indices(...): Remove indices that do not appear in any terms.

qubit_operator_sparse(...): Initialize a Scipy sparse matrix from a QubitOperator.

qubit_operator_to_pauli_sum(...): Convert QubitOperator to a sum of PauliString.

random_antisymmetric_matrix(...): Generate a random n x n antisymmetric matrix.

random_diagonal_coulomb_hamiltonian(...): Generate a random instance of DiagonalCoulombHamiltonian.

random_hermitian_matrix(...): Generate a random n x n Hermitian matrix.

random_interaction_operator(...): Generate a random instance of InteractionOperator.

random_interaction_operator_term(...): Generates a random interaction operator with non-zero coefficients only on terms corresponding to the given number of unique orbitals.

random_quadratic_hamiltonian(...): Generate a random instance of QuadraticHamiltonian.

random_qubit_operator(...)

random_unitary_matrix(...): Obtain a random n x n unitary matrix.

reduce_number_of_terms(...): Reduce the number of Pauli strings of operator using stabilizers.

reorder(...): Changes the ladder operator order of the Hamiltonian based on the provided order_function per mode index.

reverse_jordan_wigner(...): Transforms a QubitOperator into a FermionOperator using the Jordan-Wigner transform.

rhf_func_generator(...): Generate the energy, gradient, and unitary functions

rhf_minimization(...): Perform Hartree-Fock energy minimization

rhf_params_to_matrix(...): For restricted Hartree-Fock we have nocc * nvirt parameters.

rot11(...): Phases the |11> state of two qubits by e^{i rads}.

rot111(...): Phases the |111> state of three qubits by e^{i rads}.

rotate_qubit_by_pauli(...): Rotate qubit operator by exponential of Pauli.

s_plus_operator(...): Return the s+ operator.

s_squared_operator(...): Return the s^{2} operator.

save_operator(...): Save FermionOperator or QubitOperator to file.

shift_decoder(...): Shifts the indices of a decoder by a constant.

simulate_trotter(...): Simulate Hamiltonian evolution using a Trotter-Suzuki product formula.

simulation_ordered_grouped_hubbard_terms_with_info(...): Give terms from the Fermi-Hubbard Hamiltonian in simulated order.

simulation_ordered_grouped_low_depth_terms_with_info(...): Give terms from the dual basis Hamiltonian in simulated order.

single_quad_op_sparse(...): Make a matrix representation of a singular quadrature operator in the Fock space.

singlet_erpa(...): Generate the singlet ERPA equations

slater_determinant_preparation_circuit(...): Obtain the description of a circuit which prepares a Slater determinant.

sparse_eigenspectrum(...): Perform a dense diagonalization.

split_operator_trotter_error_operator_diagonal_two_body(...): Compute the split-operator Trotter error of a diagonal two-body Hamiltonian.

stagger_with_info(...): Give terms simulated in a single stagger of a Trotter step.

state_swap_eigen_component(...): The +/- eigen-component of the operation that swaps states x and y.

sum_of_interaction_operator_gate_generators(...): The interaction operator that is the sum of the generators of the specified fermionic simulation gates.

swap_columns(...): Swap columns i and j of matrix M.

swap_network(...): Apply operations to pairs of qubits or modes using a swap network.

swap_rows(...): Swap rows i and j of matrix M.

sx_operator(...): Return the sx operator.

sy_operator(...): Return the sy operator.

symmetric_ordering(...): Apply the symmetric ordering to a BosonOperator or QuadOperator.

symmetry_conserving_bravyi_kitaev(...): Returns the qubit Hamiltonian for the fermionic Hamiltonian supplied, with two qubits removed using conservation of electron spin and number, as described in arXiv:1701.08213.

sz_operator(...): Return the sz operator.

taper_off_qubits(...): Remove qubits from given operator.

trivially_commutes_dual_basis(...): Determine whether the given terms trivially commute.

trivially_double_commutes_dual_basis(...): Check if the double commutator [term_a, [term_b, term_c]] is zero.

trivially_double_commutes_dual_basis_using_term_info(...): Return whether [op_a, [op_b, op_a_prime]] is trivially zero.

trotter_operator_grouping(...): Trotter-decomposes operators into groups without exponentiating.

trotter_steps_required(...): Determine the number of Trotter steps for accurate simulation.

trotterize_exp_qubop_to_qasm(...): Trotterize a Qubit hamiltonian and write it to QASM format.

tunneling_operator(...)

two_body_fermion_constraints(...): Generates two-body positivity constraints on fermionic RDMs.

uccsd_convert_amplitude_format(...): Re-format single_amplitudes and double_amplitudes from ndarrays to lists.

uccsd_generator(...): Create a fermionic operator that is the generator of uccsd.

uccsd_singlet_generator(...): Create a singlet UCCSD generator for a system with n_electrons

uccsd_singlet_get_packed_amplitudes(...): Convert amplitudes for use with singlet UCCSD

uccsd_singlet_paramsize(...): Determine number of independent amplitudes for singlet UCCSD

unlinearize_term(...): Function to return integer index of term indices.

up_index(...): Function to return up-orbital index given a spatial orbital index.

up_then_down(...): up then down reordering, given the operator has the default even-odd ordering.

valdemoro_reconstruction(...): Build a 3-RDM by cumulant expansion and setting 3rd cumulant to zero

validate_trotterized_evolution(...): Checks whether a circuit implements Trotterized evolution

variance(...): Compute variance of operator with a state.

vector_to_operator(...): Function to map vector to operator.

verstraete_cirac_2d_square(...): Apply the Verstraete-Cirac transform on a 2-d square lattice.

vertical_edges_snake(...): Obtain the vertical edges in the 2-d snake ordering.

vpe_circuits_single_timestep(...): Prepares the circuits to perform VPE at a fixed time

vpe_single_circuit(...): Combines the different parts that make up a VPE circuit

wedge(...): Implement the wedge product between left_tensor and right_tensor

weight_one_binary_addressing_code(...): Weight-1 binary addressing code (arXiv:1712.07067).

weight_one_segment_code(...): Weight-1 segment code (arXiv:1712.07067).

weight_two_segment_code(...): Weight-2 segment code (arXiv:1712.07067).

weyl_polynomial_quantization(...): Apply the Weyl quantization to a phase space polynomial.

wigner_seitz_length_scale(...): Function to give length_scale associated with Wigner-Seitz radius.

wrapped_kronecker(...): Return the Kronecker product of two sparse.csc_matrix operators.

{
 '?': 0,
 'Ac': 89,
 'Ag': 47,
 'Al': 13,
 'Am': 95,
 'Ar': 18,
 'As': 33,
 'At': 85,
 'Au': 79,
 'B': 5,
 'Ba': 56,
 'Be': 4,
 'Bi': 83,
 'Bk': 97,
 'Br': 35,
 'C': 6,
 'Ca': 20,
 'Cd': 48,
 'Ce': 58,
 'Cf': 98,
 'Cl': 17,
 'Cm': 96,
 'Co': 27,
 'Cr': 24,
 'Cs': 55,
 'Cu': 29,
 'Dy': 66,
 'Er': 68,
 'Es': 99,
 'Eu': 63,
 'F': 9,
 'Fe': 26,
 'Fm': 100,
 'Fr': 87,
 'Ga': 31,
 'Gd': 64,
 'Ge': 32,
 'H': 1,
 'He': 2,
 'Hf': 72,
 'Hg': 80,
 'Ho': 67,
 'I': 53,
 'In': 49,
 'Ir': 77,
 'K': 19,
 'Kr': 36,
 'La': 57,
 'Li': 3,
 'Lr': 103,
 'Lu': 71,
 'Md': 101,
 'Mg': 12,
 'Mn': 25,
 'Mo': 42,
 'N': 7,
 'Na': 11,
 'Nb': 41,
 'Nd': 60,
 'Ne': 10,
 'Ni': 28,
 'No': 102,
 'Np': 93,
 'O': 8,
 'Os': 76,
 'P': 15,
 'Pa': 91,
 'Pb': 82,
 'Pd': 46,
 'Pm': 61,
 'Po': 84,
 'Pr': 59,
 'Pt': 78,
 'Pu': 94,
 'Ra': 88,
 'Rb': 37,
 'Re': 75,
 'Rh': 45,
 'Rn': 86,
 'Ru': 44,
 'S': 16,
 'Sb': 51,
 'Sc': 21,
 'Se': 34,
 'Si': 14,
 'Sm': 62,
 'Sn': 50,
 'Sr': 38,
 'Ta': 73,
 'Tb': 65,
 'Tc': 43,
 'Te': 52,
 'Th': 90,
 'Ti': 22,
 'Tl': 81,
 'Tm': 69,
 'U': 92,
 'V': 23,
 'W': 74,
 'Xe': 54,
 'Y': 39,
 'Yb': 70,
 'Zn': 30,
 'Zr': 40
}