Learning t-doped stabilizer states
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916263065812992 |
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| author | Leone, Lorenzo Oliviero, Salvatore F. E. Hamma, Alioscia |
| author_facet | Leone, Lorenzo Oliviero, Salvatore F. E. Hamma, Alioscia |
| contents | In this paper, we present a learning algorithm aimed at learning states obtained from computational basis states by Clifford circuits doped with a finite number $t$ of $T$-gates. The algorithm learns an exact tomographic description of $t$-doped stabilizer states in terms of Pauli observables. This is possible because such states are countable and form a discrete set. To tackle the problem, we introduce a novel algebraic framework for $t$-doped stabilizer states, which extends beyond $T$-gates and includes doping with any kind of local non-Clifford gate. The algorithm requires resources of complexity $\text{poly}(n,2^t)$ and exhibits an exponentially small probability of failure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_15398 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Learning t-doped stabilizer states Leone, Lorenzo Oliviero, Salvatore F. E. Hamma, Alioscia Quantum Physics In this paper, we present a learning algorithm aimed at learning states obtained from computational basis states by Clifford circuits doped with a finite number $t$ of $T$-gates. The algorithm learns an exact tomographic description of $t$-doped stabilizer states in terms of Pauli observables. This is possible because such states are countable and form a discrete set. To tackle the problem, we introduce a novel algebraic framework for $t$-doped stabilizer states, which extends beyond $T$-gates and includes doping with any kind of local non-Clifford gate. The algorithm requires resources of complexity $\text{poly}(n,2^t)$ and exhibits an exponentially small probability of failure. |
| title | Learning t-doped stabilizer states |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2305.15398 |