# Towards large-scale quantum optimization solvers with few qubits

**Authors:** Marco Sciorilli, Lucas Borges, Taylor L. Patti, Diego García-Martín, Giancarlo Camilo, Anima Anandkumar, Leandro Aolita  
**arXiv:** [2401.09421](https://arxiv.org/abs/2401.09421)  
**Date:** 2024-01-17  
**Summary page:** https://www.summarizepaper.com/fr/arxiv-id/2401.09421v1/

## Abstract

We introduce a variational quantum solver for combinatorial optimizations over $m=\mathcal{O}(n^k)$ binary variables using only $n$ qubits, with tunable $k>1$. The number of parameters and circuit depth display mild linear and sublinear scalings in $m$, respectively. Moreover, we analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature. This leads to unprecedented quantum-solver performances. For $m=7000$, numerical simulations produce solutions competitive in quality with state-of-the-art classical solvers. In turn, for $m=2000$, an experiment with $n=17$ trapped-ion qubits featured MaxCut approximation ratios estimated to be beyond the hardness threshold $0.941$. To our knowledge, this is the highest quality attained experimentally on such sizes. Our findings offer a novel heuristics for quantum-inspired solvers as well as a promising route towards solving commercially-relevant problems on near term quantum devices.