Toward Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU($d$) Symmetry
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917096649129984 |
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| author | Zheng, Han Li, Zimu Strelchuk, Sergii Kondor, Risi Liu, Junyu |
| author_facet | Zheng, Han Li, Zimu Strelchuk, Sergii Kondor, Risi Liu, Junyu |
| contents | We introduce a framework of the equivariant convolutional quantum algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU$(d)$ symmetries. It allows us to enhance a natural model of quantum computation -- permutational quantum computing (PQC) -- and define a more powerful model: PQC+. While PQC was shown to be efficiently classically simulatable, we exhibit a problem which can be efficiently solved on PQC+ machine, whereas no classical polynomial time algorithm is known; thus providing evidence against PQC+ being classically simulatable. We further discuss practical quantum machine learning algorithms which can be carried out in the paradigm of PQC+. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_07250 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Toward Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU($d$) Symmetry Zheng, Han Li, Zimu Strelchuk, Sergii Kondor, Risi Liu, Junyu Quantum Physics Artificial Intelligence Machine Learning Mathematical Physics We introduce a framework of the equivariant convolutional quantum algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU$(d)$ symmetries. It allows us to enhance a natural model of quantum computation -- permutational quantum computing (PQC) -- and define a more powerful model: PQC+. While PQC was shown to be efficiently classically simulatable, we exhibit a problem which can be efficiently solved on PQC+ machine, whereas no classical polynomial time algorithm is known; thus providing evidence against PQC+ being classically simulatable. We further discuss practical quantum machine learning algorithms which can be carried out in the paradigm of PQC+. |
| title | Toward Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU($d$) Symmetry |
| topic | Quantum Physics Artificial Intelligence Machine Learning Mathematical Physics |
| url | https://arxiv.org/abs/2207.07250 |