Towards large-scale quantum optimization solvers with few qubits
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916651991040000 |
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| author | Sciorilli, Marco Borges, Lucas Patti, Taylor L. García-Martín, Diego Camilo, Giancarlo Anandkumar, Anima Aolita, Leandro |
| author_facet | Sciorilli, Marco Borges, Lucas Patti, Taylor L. García-Martín, Diego Camilo, Giancarlo Anandkumar, Anima Aolita, Leandro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09421 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards large-scale quantum optimization solvers with few qubits Sciorilli, Marco Borges, Lucas Patti, Taylor L. García-Martín, Diego Camilo, Giancarlo Anandkumar, Anima Aolita, Leandro Quantum Physics 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. |
| title | Towards large-scale quantum optimization solvers with few qubits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.09421 |