Agnostic Tomography of Stabilizer Product States
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910055380549632 |
|---|---|
| author | Grewal, Sabee Iyer, Vishnu Kretschmer, William Liang, Daniel |
| author_facet | Grewal, Sabee Iyer, Vishnu Kretschmer, William Liang, Daniel |
| contents | We define a quantum learning task called agnostic tomography, where given copies of an arbitrary state $ρ$ and a class of quantum states $\mathcal{C}$, the goal is to output a succinct description of a state that approximates $ρ$ at least as well as any state in $\mathcal{C}$ (up to some small error $\varepsilon$). This task generalizes ordinary quantum tomography of states in $\mathcal{C}$ and is more challenging because the learning algorithm must be robust to perturbations of $ρ$.
We give an efficient agnostic tomography algorithm for the class $\mathcal{C}$ of $n$-qubit stabilizer product states. Assuming $ρ$ has fidelity at least $τ$ with a stabilizer product state, the algorithm runs in time $n^{O(\log(2/τ))} / \varepsilon^2$, which is $\mathsf{poly}(n/\varepsilon)$ for any constant $τ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03813 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Agnostic Tomography of Stabilizer Product States Grewal, Sabee Iyer, Vishnu Kretschmer, William Liang, Daniel Quantum Physics Machine Learning We define a quantum learning task called agnostic tomography, where given copies of an arbitrary state $ρ$ and a class of quantum states $\mathcal{C}$, the goal is to output a succinct description of a state that approximates $ρ$ at least as well as any state in $\mathcal{C}$ (up to some small error $\varepsilon$). This task generalizes ordinary quantum tomography of states in $\mathcal{C}$ and is more challenging because the learning algorithm must be robust to perturbations of $ρ$. We give an efficient agnostic tomography algorithm for the class $\mathcal{C}$ of $n$-qubit stabilizer product states. Assuming $ρ$ has fidelity at least $τ$ with a stabilizer product state, the algorithm runs in time $n^{O(\log(2/τ))} / \varepsilon^2$, which is $\mathsf{poly}(n/\varepsilon)$ for any constant $τ$. |
| title | Agnostic Tomography of Stabilizer Product States |
| topic | Quantum Physics Machine Learning |
| url | https://arxiv.org/abs/2404.03813 |