Learning shallow quantum circuits
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917691120418816 |
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| author | Huang, Hsin-Yuan Liu, Yunchao Broughton, Michael Kim, Isaac Anshu, Anurag Landau, Zeph McClean, Jarrod R. |
| author_facet | Huang, Hsin-Yuan Liu, Yunchao Broughton, Michael Kim, Isaac Anshu, Anurag Landau, Zeph McClean, Jarrod R. |
| contents | Despite fundamental interests in learning quantum circuits, the existence of a computationally efficient algorithm for learning shallow quantum circuits remains an open question. Because shallow quantum circuits can generate distributions that are classically hard to sample from, existing learning algorithms do not apply. In this work, we present a polynomial-time classical algorithm for learning the description of any unknown $n$-qubit shallow quantum circuit $U$ (with arbitrary unknown architecture) within a small diamond distance using single-qubit measurement data on the output states of $U$. We also provide a polynomial-time classical algorithm for learning the description of any unknown $n$-qubit state $\lvert ψ\rangle = U \lvert 0^n \rangle$ prepared by a shallow quantum circuit $U$ (on a 2D lattice) within a small trace distance using single-qubit measurements on copies of $\lvert ψ\rangle$. Our approach uses a quantum circuit representation based on local inversions and a technique to combine these inversions. This circuit representation yields an optimization landscape that can be efficiently navigated and enables efficient learning of quantum circuits that are classically hard to simulate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10095 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning shallow quantum circuits Huang, Hsin-Yuan Liu, Yunchao Broughton, Michael Kim, Isaac Anshu, Anurag Landau, Zeph McClean, Jarrod R. Quantum Physics Information Theory Machine Learning Despite fundamental interests in learning quantum circuits, the existence of a computationally efficient algorithm for learning shallow quantum circuits remains an open question. Because shallow quantum circuits can generate distributions that are classically hard to sample from, existing learning algorithms do not apply. In this work, we present a polynomial-time classical algorithm for learning the description of any unknown $n$-qubit shallow quantum circuit $U$ (with arbitrary unknown architecture) within a small diamond distance using single-qubit measurement data on the output states of $U$. We also provide a polynomial-time classical algorithm for learning the description of any unknown $n$-qubit state $\lvert ψ\rangle = U \lvert 0^n \rangle$ prepared by a shallow quantum circuit $U$ (on a 2D lattice) within a small trace distance using single-qubit measurements on copies of $\lvert ψ\rangle$. Our approach uses a quantum circuit representation based on local inversions and a technique to combine these inversions. This circuit representation yields an optimization landscape that can be efficiently navigated and enables efficient learning of quantum circuits that are classically hard to simulate. |
| title | Learning shallow quantum circuits |
| topic | Quantum Physics Information Theory Machine Learning |
| url | https://arxiv.org/abs/2401.10095 |