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

functionals module

hamiltonians module

linalg module

measurements module

ops module: This module should contain objects that describe the algebra of various

testing module

third_party 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

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

class BinaryPolynomial: The BinaryPolynomial class provides an analytic representation

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

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

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

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

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

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

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

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

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

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

binary_partition_iterator(...): Generator for a list of 2-partitions of N qubits

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

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

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

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

bravyi_kitaev_fast(...): Find the Pauli-representation of InteractionOperator for Bravyi-Kitaev

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

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

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

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

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

error_operator(...): Determine the difference between the exact generator of unitary

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

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

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

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

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

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

fermionic_simulation_gates_from_interaction_operator(...): Given \(H = \sum_{I \subset [n]} H_I\), returns gates

fermionic_swap_trotter_error_operator_diagonal_two_body(...): Compute the fermionic swap network Trotter error of a diagonal

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

general_basis_change(...): Change the basis of an 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

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

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

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

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

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

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

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

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

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,

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

jw_sparse_particle_hole_transformation_last_mode(...): Return the matrix (acting on a full wavefunction) that performs a

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

low_depth_second_order_trotter_error_operator(...): Determine the difference between the exact generator of unitary

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

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,

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

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

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. This code is

partition_iterator(...): Generator for a list of k-partitions of N qubits such that

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

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

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

reverse_jordan_wigner(...): Transforms a QubitOperator into a FermionOperator using the

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. These are

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

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

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

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

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

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

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). This highly

weight_one_segment_code(...): Weight-1 segment code (arXiv:1712.07067). Outputs a 3-mode, 2-qubit

weight_two_segment_code(...): Weight-2 segment code (arXiv:1712.07067). Outputs a 5-mode, 4-qubit

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
}