---
title: double_factorized_t2 (latest version)
description: API reference for qiskit_fermions.linalg.double_factorized_t2 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
---

# double\_factorized\_t2

`double_factorized_t2(t2_amplitudes, tol, max_terms=None)`

Double-factorized decomposition of spin-restricted $t_2$ amplitudes.

Factorizes $t_{ijab}$ (with $i, j$ occupied and $a, b$ virtual) into a list of $(Z, U)$ terms suitable for reconstruction by [`reconstruct_t2()`](/docs/api/qiskit-fermions/linalg-reconstruct-t-2 "qiskit_fermions.linalg.reconstruct_t2"). The number of terms is truncated to `max_terms` (default: all).

**Parameters**

- **t2\_amplitudes** – the $t_2$ amplitudes of shape `(nocc, nocc, nvrt, nvrt)`.
- **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 $(Z, U)$ 2-tuples, where `Z` is the diagonal Coulomb matrix and `U` is the orbital rotation.