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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.16693 |
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| _version_ | 1866915334382944256 |
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| author | Vasconcelos, Francisca Huang, Hsin-Yuan |
| author_facet | Vasconcelos, Francisca Huang, Hsin-Yuan |
| contents | We present the first computationally-efficient algorithm for average-case learning of shallow quantum circuits with many-qubit gates. Specifically, we provide a quasi-polynomial time and sample complexity algorithm for learning unknown QAC$^0$ circuits -- constant-depth circuits with arbitrary single-qubit gates and polynomially many $CZ$ gates of unbounded width -- with at most logarithmic ancilla, up to inverse-polynomially small error. Furthermore, we show that the learned unitary can be efficiently synthesized in poly-logarithmic depth. This work expands the family of efficiently learnable quantum circuits, notably since in finite-dimensional circuit geometries, QAC$^0$ circuits require polynomial depth to implement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16693 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning shallow quantum circuits with many-qubit gates Vasconcelos, Francisca Huang, Hsin-Yuan Quantum Physics We present the first computationally-efficient algorithm for average-case learning of shallow quantum circuits with many-qubit gates. Specifically, we provide a quasi-polynomial time and sample complexity algorithm for learning unknown QAC$^0$ circuits -- constant-depth circuits with arbitrary single-qubit gates and polynomially many $CZ$ gates of unbounded width -- with at most logarithmic ancilla, up to inverse-polynomially small error. Furthermore, we show that the learned unitary can be efficiently synthesized in poly-logarithmic depth. This work expands the family of efficiently learnable quantum circuits, notably since in finite-dimensional circuit geometries, QAC$^0$ circuits require polynomial depth to implement. |
| title | Learning shallow quantum circuits with many-qubit gates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.16693 |