| Autor: |
Huggins, William J., Wan, Kianna, McClean, Jarrod, O'Brien, Thomas E., Wiebe, Nathan, Babbush, Ryan |
| Rok vydání: |
2021 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| DOI: |
10.1103/PhysRevLett.129.240501 |
| Popis: |
Many quantum algorithms involve the evaluation of expectation values. Optimal strategies for estimating a single expectation value are known, requiring a number of state preparations that scales with the target error $\varepsilon$ as $\mathcal{O}(1/\varepsilon)$. In this paper, we address the task of estimating the expectation values of $M$ different observables, each to within additive error $\varepsilon$, with the same $1/\varepsilon$ dependence. We describe an approach that leverages Gily\'en et al.'s quantum gradient estimation algorithm to achieve $\mathcal{O}(\sqrt{M}/\varepsilon)$ scaling up to logarithmic factors, regardless of the commutation properties of the $M$ observables. We prove that this scaling is worst-case optimal in the high-precision regime if the state preparation is treated as a black box, even when the operators are mutually commuting. We highlight the flexibility of our approach by presenting several generalizations, including a strategy for accelerating the estimation of a collection of dynamic correlation functions. |
| Databáze: |
arXiv |
| Externí odkaz: |
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