Tolerant Testing of Stabilizer States with Mixed State Inputs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908358591643648 |
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| author | Iyer, Vishnu Liang, Daniel |
| author_facet | Iyer, Vishnu Liang, Daniel |
| contents | We study the problem of tolerant testing of stabilizer states. In particular, we give the first such algorithm that accepts mixed state inputs. Formally, given a mixed state $ρ$ that either has fidelity at least $\varepsilon_1$ with some stabilizer pure state or fidelity at most $\varepsilon_2$ with all such states, where $\varepsilon_2 \leq \varepsilon_1^{O(1)}$, our algorithm distinguishes the two cases with sample complexity $\text{poly}(1/\varepsilon_1)$ and time complexity $O(n \cdot \text{poly}(1/\varepsilon_1))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08765 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tolerant Testing of Stabilizer States with Mixed State Inputs Iyer, Vishnu Liang, Daniel Quantum Physics Data Structures and Algorithms We study the problem of tolerant testing of stabilizer states. In particular, we give the first such algorithm that accepts mixed state inputs. Formally, given a mixed state $ρ$ that either has fidelity at least $\varepsilon_1$ with some stabilizer pure state or fidelity at most $\varepsilon_2$ with all such states, where $\varepsilon_2 \leq \varepsilon_1^{O(1)}$, our algorithm distinguishes the two cases with sample complexity $\text{poly}(1/\varepsilon_1)$ and time complexity $O(n \cdot \text{poly}(1/\varepsilon_1))$. |
| title | Tolerant Testing of Stabilizer States with Mixed State Inputs |
| topic | Quantum Physics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2411.08765 |