Quantum Neural Estimation of Entropies
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911812616716288 |
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| author | Goldfeld, Ziv Patel, Dhrumil Sreekumar, Sreejith Wilde, Mark M. |
| author_facet | Goldfeld, Ziv Patel, Dhrumil Sreekumar, Sreejith Wilde, Mark M. |
| contents | Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy measures. Here we propose a variational quantum algorithm for estimating the von Neumann and Rényi entropies, as well as the measured relative entropy and measured Rényi relative entropy. Our approach first parameterizes a variational formula for the measure of interest by a quantum circuit and a classical neural network, and then optimizes the resulting objective over parameter space. Numerical simulations of our quantum algorithm are provided, using a noiseless quantum simulator. The algorithm provides accurate estimates of the various entropy measures for the examples tested, which renders it as a promising approach for usage in downstream tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01171 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum Neural Estimation of Entropies Goldfeld, Ziv Patel, Dhrumil Sreekumar, Sreejith Wilde, Mark M. Quantum Physics Statistical Mechanics Information Theory Machine Learning Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy measures. Here we propose a variational quantum algorithm for estimating the von Neumann and Rényi entropies, as well as the measured relative entropy and measured Rényi relative entropy. Our approach first parameterizes a variational formula for the measure of interest by a quantum circuit and a classical neural network, and then optimizes the resulting objective over parameter space. Numerical simulations of our quantum algorithm are provided, using a noiseless quantum simulator. The algorithm provides accurate estimates of the various entropy measures for the examples tested, which renders it as a promising approach for usage in downstream tasks. |
| title | Quantum Neural Estimation of Entropies |
| topic | Quantum Physics Statistical Mechanics Information Theory Machine Learning |
| url | https://arxiv.org/abs/2307.01171 |