Convert two-body operator into sum of squared one-body operators.
openfermion.circuits.low_rank_two_body_decomposition(
two_body_coefficients,
truncation_threshold=1e-08,
final_rank=None,
spin_basis=True
)
As in arXiv:1808.02625, this function decomposes
\(\sum_{pqrs} h_{pqrs} a^\dagger_p a^\dagger_q a_r a_s\) as
\(\sum_{l} \lambda_l (\sum_{pq} g_{lpq} a^\dagger_p a_q)^2\)
l is truncated to take max value L so that
\(\sum_{l=0}^{L-1} (\sum_{pq} |g_{lpq}|)^2 |\lambda_l| < x\)
Args |
two_bodycoefficients (ndarray): an N x N x N x N
numpy array giving the \(h{pqrs}\) tensor.
This tensor must be 8-fold symmetric (real integrals).
truncation_threshold (optional Float): the value of x, above.
final_rank (optional int): if provided, this specifies the value of
L at which to truncate. This overrides truncation_threshold.
spin_basis (bool): True if the two-body terms are passed in spin
orbital basis. False if already in spatial orbital basis.
|
Returns |
eigenvalues (ndarray of floats): length L array
giving the \(\lambda_l\).
one_bodysquares (ndarray of floats): L x N x N array of floats
corresponding to the value of \(g{pql}\).
one_body_correction (ndarray): One-body correction terms that result
from reordering to chemist ordering, in spin-orbital basis.
truncationvalue (float): after truncation, this is the value
\(\sum{l=0}^{L-1} (\sum{pq} |g{lpq}|)^2 |\lambda_l| < x\)
|
Raises |
TypeError
|
Invalid two-body coefficient tensor specification.
|