---
title: double_factorized_t2_alpha_beta (latest version)
description: API reference for qiskit_fermions.linalg.double_factorized_t2_alpha_beta in the latest version of qiskit-fermions
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit-fermions/linalg-double-factorized-t-2-alpha-beta
---

# double\_factorized\_t2\_alpha\_beta

`double_factorized_t2_alpha_beta(t2_amplitudes, tol, max_terms=None)`

Double-factorized decomposition of alpha-beta (spin-unrestricted) $t_2$ amplitudes.

Returns a list of terms suitable for reconstruction by [`reconstruct_t2_alpha_beta()`](/docs/api/qiskit-fermions/linalg-reconstruct-t-2-alpha-beta "qiskit_fermions.linalg.reconstruct_t2_alpha_beta"). The number of terms is truncated to `max_terms` (default: all).

**Parameters**

- **t2\_amplitudes** – the alpha-beta $t_2$ amplitudes of shape `(nocc_a, nocc_b, nvrt_a, nvrt_b)`.
- **tol** – the tolerance controlling the truncation error of the decomposition.
- **max\_terms** – the maximum number of terms to retain. Defaults to all.

**Returns**

A list of 2-tuples, each consisting of

- a 3-tuple of the diagonal Coulomb matrices in the order `(aa, ab, bb)`
- a 2-tuple of the orbital rotations in the order `(alpha, beta)`