Biased Estimator Channels for Classical Shadows
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915222371958784 |
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| author | Cai, Zhenyu Chapman, Adrian Jnane, Hamza Koczor, Bálint |
| author_facet | Cai, Zhenyu Chapman, Adrian Jnane, Hamza Koczor, Bálint |
| contents | Extracting classical information from quantum systems is of fundamental importance, and classical shadows allow us to extract a large amount of information using relatively few measurements. Conventional shadow estimators are unbiased and thus approach the true mean in the infinite-sample limit. In this work, we consider a biased scheme, intentionally introducing a bias by rescaling the conventional classical shadows estimators can reduce the error in the finite-sample regime. The approach is straightforward to implement and requires no quantum resources. We analytically prove average case as well as worst- and best-case scenarios, and rigorously prove that it is, in principle, always worth biasing the estimators. We illustrate our approach in a quantum simulation task of a $12$-qubit spin-ring problem and demonstrate how estimating expected values of non-local perturbations can be significantly more efficient using our biased scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09511 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Biased Estimator Channels for Classical Shadows Cai, Zhenyu Chapman, Adrian Jnane, Hamza Koczor, Bálint Quantum Physics Extracting classical information from quantum systems is of fundamental importance, and classical shadows allow us to extract a large amount of information using relatively few measurements. Conventional shadow estimators are unbiased and thus approach the true mean in the infinite-sample limit. In this work, we consider a biased scheme, intentionally introducing a bias by rescaling the conventional classical shadows estimators can reduce the error in the finite-sample regime. The approach is straightforward to implement and requires no quantum resources. We analytically prove average case as well as worst- and best-case scenarios, and rigorously prove that it is, in principle, always worth biasing the estimators. We illustrate our approach in a quantum simulation task of a $12$-qubit spin-ring problem and demonstrate how estimating expected values of non-local perturbations can be significantly more efficient using our biased scheme. |
| title | Biased Estimator Channels for Classical Shadows |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.09511 |