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1. Quantum microgrid state estimation

   https://doi.org/10.1016/j.epsr.2022.108386  

   Feng, Fei; Zhang, Peng; Zhou, Yifan; Tang, Zefan (November 2022, Electric Power Systems Research)
2. Reductive quantum phase estimation

   https://doi.org/10.1103/PhysRevResearch.6.033051  

   Papadopoulos, Nicholas_J C; Reilly, Jarrod T; Wilson, John Drew; Holland, Murray J (July 2024, Physical Review Research)

   Estimating a quantum phase is a necessary task in a wide range of fields of quantum science. To accomplish this task, two well-known methods have been developed in distinct contexts, namely, Ramsey interferometry (RI) in atomic and molecular physics and quantum phase estimation (QPE) in quantum computing. We demonstrate that these canonical examples are instances of a larger class of phase estimation protocols, which we call reductive quantum phase estimation (RQPE) circuits. Here, we present an explicit algorithm that allows one to create an RQPE circuit. This circuit distinguishes an arbitrary set of phases with a smaller number of qubits and unitary applications, thereby solving a general class of quantum hypothesis testing to which RI and QPE belong. We further demonstrate a tradeoff between measurement precision and phase distinguishability, which allows one to tune the circuit to be optimal for a specific application. Published by the American Physical Society2024 

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3. Distributed Quantum inner product estimation

   https://doi.org/10.1145/3519935.3519974  

   Anshu, Anurag; Landau, Zeph; Liu, Yunchao (June 2022, Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing)
4. Quantum neural estimation of entropies

   https://doi.org/10.1103/PhysRevA.109.032431  

   Goldfeld, Ziv; Patel, Dhrumil; Sreekumar, Sreejith; Wilde, Mark_M (March 2024, Physical Review A)
5. Quantum Query Complexity of Entropy Estimation

   https://doi.org/10.1109/TIT.2018.2883306  

   Li, Tongyang; Wu, Xiaodi (April 2019, IEEE Transactions on Information Theory)

   Estimation of Shannon and Rényi entropies of unknown discrete distributions is a fundamental problem in statistical property testing. In this paper, we give the first quantum algorithms for estimating α-Rényi entropies (Shannon entropy being 1-Rényi entropy). In particular, we demonstrate a quadratic quantum speedup for Shannon entropy estimation and a generic quantum speedup for α-Rényi entropy estimation for all α ≥ 0, including tight bounds for the Shannon entropy, the Hartley entropy (α = 0), and the collision entropy (α = 2). We also provide quantum upper bounds for estimating min-entropy (α = +∞) as well as the Kullback-Leibler divergence. We complement our results with quantum lower bounds on α- Rényi entropy estimation for all α ≥ 0. Our approach is inspired by the pioneering work of Bravyi, Harrow, and Hassidim (BHH) [1], however, with many new technical ingredients: (1) we improve the error dependence of the BHH framework by a fine-tuned error analysis together with Montanaro’s approach to estimating the expected output of quantum subroutines [2] for α = 0, 1; (2) we develop a procedure, similar to cooling schedules in simulated annealing, for general α ≥ 0; (3) in the cases of integer α ≥ 2 and α = +∞, we reduce the entropy estimation problem to the α-distinctness and the ⌈log n⌉-distinctness problems, respectively. 

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