Principal eigenstate classical shadows |
Original Papers |
Given many copies of an unknown quantum state $\rho$, we consider the task of learning a classical description of its principal eigenstate. Namely, assuming that $\rho$ has an eigenstate $|\phi⟩$ with (unknown) eigenvalue $\lambda > 1/2$, the goal is to learn a (classical shadows style) classical description of $|\phi⟩$ which can later be used to estimate expectation values $⟨\phi |O | \phi ⟩$ for any $O$ in some class of observables. We consider the sample-complexity setting in which generating a copy of $\rho$ is expensive, but joint measurements on many copies of the state are possible. We present a protocol for this task scaling with the principal eigenvalue $\lambda$ and show that it is optimal within a space of natural approaches, e.g., applying quantum state purification followed by a single-copy classical shadows scheme. Furthermore, when $\lambda$ is sufficiently close to $1$, the performance of our algorithm is optimal—matching the sample complexity for pure state classical shadows. |
inproceedings |
Proceedings of Machine Learning Research |
PMLR |
2640-3498 |
grier24a |
0 |
Principal eigenstate classical shadows |
2122 |
2165 |
2122-2165 |
2122 |
false |
Grier, Daniel and Pashayan, Hakop and Schaeffer, Luke |
| given |
family |
Daniel |
Grier |
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| given |
family |
Hakop |
Pashayan |
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| given |
family |
Luke |
Schaeffer |
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2024-06-30 |
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Proceedings of Thirty Seventh Conference on Learning Theory |
247 |
inproceedings |
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