Amplified Amplitude Estimation: Exploiting Prior Knowledge to Improve Estimates of Expectation Values
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911787058724864 |
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| author | Simon, Sophia Degroote, Matthias Moll, Nikolaj Santagati, Raffaele Streif, Michael Wiebe, Nathan |
| author_facet | Simon, Sophia Degroote, Matthias Moll, Nikolaj Santagati, Raffaele Streif, Michael Wiebe, Nathan |
| contents | We provide a method for estimating the expectation value of an operator that can utilize prior knowledge to accelerate the learning process on a quantum computer. Specifically, suppose we have an operator that can be expressed as a concise sum of projectors whose expectation values we know a priori to be $O(ε)$. In that case, we can estimate the expectation value of the entire operator within error $ε$ using a number of quantum operations that scales as $O(1/\sqrtε)$. We then show how this can be used to reduce the cost of learning a potential energy surface in quantum chemistry applications by exploiting information gained from the energy at nearby points. Furthermore, we show, using Newton-Cotes methods, how these ideas can be exploited to learn the energy via integration of derivatives that we can estimate using a priori knowledge. This allows us to reduce the cost of energy estimation if the block-encodings of directional derivative operators have a smaller normalization constant than the Hamiltonian of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Amplified Amplitude Estimation: Exploiting Prior Knowledge to Improve Estimates of Expectation Values Simon, Sophia Degroote, Matthias Moll, Nikolaj Santagati, Raffaele Streif, Michael Wiebe, Nathan Quantum Physics We provide a method for estimating the expectation value of an operator that can utilize prior knowledge to accelerate the learning process on a quantum computer. Specifically, suppose we have an operator that can be expressed as a concise sum of projectors whose expectation values we know a priori to be $O(ε)$. In that case, we can estimate the expectation value of the entire operator within error $ε$ using a number of quantum operations that scales as $O(1/\sqrtε)$. We then show how this can be used to reduce the cost of learning a potential energy surface in quantum chemistry applications by exploiting information gained from the energy at nearby points. Furthermore, we show, using Newton-Cotes methods, how these ideas can be exploited to learn the energy via integration of derivatives that we can estimate using a priori knowledge. This allows us to reduce the cost of energy estimation if the block-encodings of directional derivative operators have a smaller normalization constant than the Hamiltonian of the system. |
| title | Amplified Amplitude Estimation: Exploiting Prior Knowledge to Improve Estimates of Expectation Values |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.14791 |