# Towards Arbitrary QUBO Optimization: Analysis of Classical and Quantum-Activated Feedforward Neural Networks

arXiv: https://arxiv.org/abs/2410.12636 · HTML: https://mlsanity.com/paper/2410.12636/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 106 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Builds on (most cited first, 12 of 12)

- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [The Power of Depth for Feedforward Neural Networks](https://mlsanity.com/paper/1512.03965/) (2015)
- [A Sufficient Condition for Convergences of Adam and RMSProp](https://mlsanity.com/paper/1811.09358/) (2018)
- [Application of Quantum Annealing to Training of Deep Neural Networks](https://mlsanity.com/paper/1510.06356/) (2015)
- [Traffic flow optimization using a quantum annealer](https://mlsanity.com/paper/1708.01625/) (2017)
- [Preparation of ordered states in ultra-cold gases using Bayesian optimization](https://mlsanity.com/paper/2001.03520/) (2020)
- [Insights on Training Neural Networks for QUBO Tasks](https://mlsanity.com/paper/2004.14036/) (2020)
- [Solving Quadratic Unconstrained Binary Optimization with divide-and-conquer and quantum algorithms](https://mlsanity.com/paper/2101.07813/) (2021)
- [Diverse Adaptive Bulk Search: a Framework for Solving QUBO Problems on Multiple GPUs](https://mlsanity.com/paper/2207.03069/) (2022)
- [Integer Programming Using A Single Atom](https://mlsanity.com/paper/2402.16541/) (2024)
- [Solving The Travelling Salesman Problem Using A Single Qubit](https://mlsanity.com/paper/2407.17207/) (2024)

## Abstract (arXiv)

Quadratic Unconstrained Binary Optimization (QUBO) sits at the heart of many industries and academic fields such as logistics, supply chain, finance, pharmaceutical science, chemistry, IT, and energy sectors, among others. These problems typically involve optimizing a large number of binary variables, which makes finding exact solutions exponentially more difficult. Consequently, most QUBO problems are classified as NP-hard. To address this challenge, we developed a powerful feedforward neural network (FNN) optimizer for arbitrary QUBO problems. In this work, we demonstrate that the FNN optimizer can provide high-quality approximate solutions for large problems, including dense 80-variable weighted MaxCut and random QUBOs, achieving an average accuracy of over 99% in less than 1.1 seconds on an 8-core CPU. Additionally, the FNN optimizer outperformed the Gurobi optimizer by 72% on 200-variable random QUBO problems within a 100-second computation time limit, exhibiting strong potential for real-time optimization tasks. Building on this model, we explored the novel approach of integrating FNNs with a quantum annealer-based activation function to create a quantum-classical encoder-decoder (QCED) optimizer, aiming to further enhance the performance of FNNs in QUBO optimization.