This is a repository for the article "Higher-order quantum computing with known input states, Vanessa Brzić, Satoshi Yoshida, Mio Murao, Marco Túlio Quintino, arXiv:2510.20530 [quant-ph]".

The MATLAB code from this repository requires:

• cvx - MATLAB toolbox for optimization modeling
• QETLAB - a free open source MATLAB toolbox for quantum entanglement theory
• HigherOrderProjectors - repository from the paper arXiv:2305.01247 [quant-ph] which includes projectors on the linear space spanned by various classes higher-order transformations. (For convenience, this repository is incuded in the auxliary files of the HOQO_KS repository)

This code also requires an SDP solver which is compatible with cvx. It may be any solver, but for better performance, we suggest MOSEK.

• MOSEK - a software package for solving mathematical optimization problems (under the free personal academic license)

This repository consists of two main scripts:

• HOQO_KN_det.m: Script that evalutes the optimal performance for deterministic HOQO_KS.

• HOQO_KN_prob.m: Script that evalutes the optimal performance for probabilistic HOQO_KS.

Both scripts make use of some auxiliary files available at auxiliary, which includes the repository of HigherOrderProjectors.