Robust sparse IQP sampling in constant depth
Fuente:
arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911869835411456 |
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| author | Paletta, Louis Leverrier, Anthony Sarlette, Alain Mirrahimi, Mazyar Vuillot, Christophe |
| author_facet | Paletta, Louis Leverrier, Anthony Sarlette, Alain Mirrahimi, Mazyar Vuillot, Christophe |
| contents | Between NISQ (noisy intermediate scale quantum) approaches without any proof of robust quantum advantage and fully fault-tolerant quantum computation, we propose a scheme to achieve a provable superpolynomial quantum advantage (under some widely accepted complexity conjectures) that is robust to noise with minimal error correction requirements. We choose a class of sampling problems with commuting gates known as sparse IQP (Instantaneous Quantum Polynomial-time) circuits and we ensure its fault-tolerant implementation by introducing the tetrahelix code. This new code is obtained by merging several tetrahedral codes (3D color codes) and has the following properties: each sparse IQP gate admits a transversal implementation, and the depth of the logical circuit can be traded for its width. Combining those, we obtain a depth-1 implementation of any sparse IQP circuit up to the preparation of encoded states. This comes at the cost of a space overhead which is only polylogarithmic in the width of the original circuit. We furthermore show that the state preparation can also be performed in constant depth with a single step of feed-forward from classical computation. Our construction thus exhibits a robust superpolynomial quantum advantage for a sampling problem implemented on a constant depth circuit with a single round of measurement and feed-forward. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_10729 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Robust sparse IQP sampling in constant depth Paletta, Louis Leverrier, Anthony Sarlette, Alain Mirrahimi, Mazyar Vuillot, Christophe Quantum Physics Between NISQ (noisy intermediate scale quantum) approaches without any proof of robust quantum advantage and fully fault-tolerant quantum computation, we propose a scheme to achieve a provable superpolynomial quantum advantage (under some widely accepted complexity conjectures) that is robust to noise with minimal error correction requirements. We choose a class of sampling problems with commuting gates known as sparse IQP (Instantaneous Quantum Polynomial-time) circuits and we ensure its fault-tolerant implementation by introducing the tetrahelix code. This new code is obtained by merging several tetrahedral codes (3D color codes) and has the following properties: each sparse IQP gate admits a transversal implementation, and the depth of the logical circuit can be traded for its width. Combining those, we obtain a depth-1 implementation of any sparse IQP circuit up to the preparation of encoded states. This comes at the cost of a space overhead which is only polylogarithmic in the width of the original circuit. We furthermore show that the state preparation can also be performed in constant depth with a single step of feed-forward from classical computation. Our construction thus exhibits a robust superpolynomial quantum advantage for a sampling problem implemented on a constant depth circuit with a single round of measurement and feed-forward. |
| title | Robust sparse IQP sampling in constant depth |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2307.10729 |