A simple lower bound for the complexity of estimating partition functions on a quantum computer
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911832297439232 |
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| author | Chen, Zherui Nannicini, Giacomo |
| author_facet | Chen, Zherui Nannicini, Giacomo |
| contents | We study the complexity of estimating the partition function $\mathsf{Z}(β)=\sum_{x\inχ} e^{-βH(x)}$ for a Gibbs distribution characterized by the Hamiltonian $H(x)$. We provide a simple and natural lower bound for quantum algorithms that solve this task by relying on reflections through the coherent encoding of Gibbs states. Our primary contribution is a $\varOmega(1/ε)$ lower bound for the number of reflections needed to estimate the partition function with a quantum algorithm. The proof is based on a reduction from the problem of estimating the Hamming weight of an unknown binary string. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02414 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A simple lower bound for the complexity of estimating partition functions on a quantum computer Chen, Zherui Nannicini, Giacomo Quantum Physics Computational Complexity Data Structures and Algorithms Statistics Theory We study the complexity of estimating the partition function $\mathsf{Z}(β)=\sum_{x\inχ} e^{-βH(x)}$ for a Gibbs distribution characterized by the Hamiltonian $H(x)$. We provide a simple and natural lower bound for quantum algorithms that solve this task by relying on reflections through the coherent encoding of Gibbs states. Our primary contribution is a $\varOmega(1/ε)$ lower bound for the number of reflections needed to estimate the partition function with a quantum algorithm. The proof is based on a reduction from the problem of estimating the Hamming weight of an unknown binary string. |
| title | A simple lower bound for the complexity of estimating partition functions on a quantum computer |
| topic | Quantum Physics Computational Complexity Data Structures and Algorithms Statistics Theory |
| url | https://arxiv.org/abs/2404.02414 |