# Quantum Approximate Optimization Algorithm applied to the binary perceptron

arXiv: https://arxiv.org/abs/2112.10219 · HTML: https://mlsanity.com/paper/2112.10219/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 67 references that are in the map.
- First posted on arXiv 19 Dec 2021.

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

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [Unreasonable Effectiveness of Learning Neural Networks: From Accessible States and Robust Ensembles to Basic Algorithmic Schemes](https://mlsanity.com/paper/1605.06444/) (2016)
- [Inverse statistical problems: from the inverse Ising problem to data science](https://mlsanity.com/paper/1702.01522/) (2017)
- [Learning through atypical "phase transitions" in overparameterized neural networks](https://mlsanity.com/paper/2110.00683/) (2021)
- [Simulating a perceptron on a quantum computer](https://mlsanity.com/paper/1412.3635/) (2014)
- [Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers](https://mlsanity.com/paper/2102.05566/) (2021)
- [Efficiency of quantum versus classical annealing in non-convex learning problems](https://mlsanity.com/paper/1706.08470/) (2017)

## Built on by (most cited first, 3 of 3)

- [Quantum HyperNetworks: Training Binary Neural Networks in Quantum Superposition](https://mlsanity.com/paper/2301.08292/) (2023)
- [Quark: A Gradient-Free Quantum Learning Framework for Classification Tasks](https://mlsanity.com/paper/2210.01311/) (2022)
- [Physics-Informed Neural Networks for an optimal counterdiabatic quantum computation](https://mlsanity.com/paper/2309.04434/) (2023)

## Abstract (arXiv)

We apply digitized Quantum Annealing (QA) and Quantum Approximate Optimization Algorithm (QAOA) to a paradigmatic task of supervised learning in artificial neural networks: the optimization of synaptic weights for the binary perceptron. At variance with the usual QAOA applications to MaxCut, or to quantum spin-chains ground state preparation, the classical Hamiltonian is characterized by highly non-local multi-spin interactions. Yet, we provide evidence for the existence of optimal smooth solutions for the QAOA parameters, which are transferable among typical instances of the same problem, and we prove numerically an enhanced performance of QAOA over traditional QA. We also investigate on the role of the QAOA optimization landscape geometry in this problem, showing that the detrimental effect of a gap-closing transition encountered in QA is also negatively affecting the performance of our implementation of QAOA.