Module: openfermion.circuits

Modules

gates module: Gates useful for simulating fermions.

lcu_util module: Utility methods for LCU circuits.

low_rank module: This module provides tools for simulating rank deficient operators.

primitives module: Building blocks of algorithms for quantum simulation.

slater_determinants module: This module contains functions for compiling circuits to prepare Slater determinants and fermionic Gaussian states.

trotter module

trotter_exp_to_qgates module: Module to perform Trotter-Suzuki decompositions to output as circuits.

unitary_cc module: Module to create and manipulate unitary coupled cluster operators.

vpe_circuits module: Circuit generation functions for verified phase estimation (2010.02538)

Classes

class AsymmetricSplitOperatorTrotterStep: A method for performing a Trotter step.

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

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

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

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

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

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

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

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

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

class SplitOperatorTrotterStep: A method for performing a Trotter step.

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).

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.

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

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.

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.

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

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

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

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

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

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.

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

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

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.

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

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

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.

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

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

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.

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

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

LINEAR_SWAP_NETWORK Instance of openfermion.circuits.LinearSwapNetworkTrotterAlgorithm
LOW_RANK Instance of openfermion.circuits.LowRankTrotterAlgorithm
SPLIT_OPERATOR Instance of openfermion.circuits.SplitOperatorTrotterAlgorithm
standard_vpe_rotation_set [[0.25, cirq.Ry(rads=1.5707963267948966), cirq.Ry(rads=-1.5707963267948966)], [-0.25, cirq.Ry(rads=1.5707963267948966), cirq.Ry(rads=1.5707963267948966)], [(-0-0.25j), cirq.Ry(rads=1.5707963267948966), cirq.Rx(rads=-1.5707963267948966)], [0.25j, cirq.Ry(rads=1.5707963267948966), cirq.Rx(rads=1.5707963267948966)], [0.25, cirq.Rx(rads=1.5707963267948966), cirq.Rx(rads=-1.5707963267948966)], [-0.25, cirq.Rx(rads=1.5707963267948966), cirq.Rx(rads=1.5707963267948966)], [0.25j, cirq.Rx(rads=1.5707963267948966), cirq.Ry(rads=-1.5707963267948966)], [(-0-0.25j), cirq.Rx(rads=1.5707963267948966), cirq.Ry(rads=1.5707963267948966)]]