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arXiv · 2401.09421

Towards large-scale quantum optimization solvers with few qubits

Marco Sciorilli·Lucas Borges·Taylor L. Patti·Diego García-Martín·Giancarlo Camilo·Anima Anandkumar·Leandro Aolita
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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.

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Marco Sciorilli, Lucas Borges, Taylor L. Patti, Diego García-Martín, Giancarlo Camilo, Anima Anandkumar, Leandro Aolita. 2024-01-17. Towards large-scale quantum optimization solvers with few qubits. https://doi.org/10.1038/s41467-024-55346-z

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