Optimal Strategies of Quantum Metrology with a Strict Hierarchy

• URL: http://arxiv.org/abs/2203.09758v2
• Date: Sat, 18 Feb 2023 13:13:44 GMT
• Title: Optimal Strategies of Quantum Metrology with a Strict Hierarchy
• Authors: Qiushi Liu, Zihao Hu, Haidong Yuan, Yuxiang Yang
• Abstract summary: We identify the ultimate precision limit of different families of strategies, including the parallel, the sequential, and the indefinite-causal-order strategies. We provide an efficient algorithm that determines an optimal strategy within the family of strategies under consideration.
• Score: 3.706744588098214
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One of the main quests in quantum metrology is to attain the ultimate precision limit with given resources, where the resources are not only of the number of queries, but more importantly of the allowed strategies. With the same number of queries, the restrictions on the strategies constrain the achievable precision. In this work, we establish a systematic framework to identify the ultimate precision limit of different families of strategies, including the parallel, the sequential, and the indefinite-causal-order strategies, and provide an efficient algorithm that determines an optimal strategy within the family of strategies under consideration. With our framework, we show there exists a strict hierarchy of the precision limits for different families of strategies.

Related papers

• Fully-Optimized Quantum Metrology: Framework, Tools, and Applications [8.98216737402976]
  The tutorial consists of a pedagogic introduction to the background and mathematical tools of optimal quantum metrology. The approach can identify the optimal precision for different sets of strategies, including parallel, sequential, quantum SWITCH-enhanced, causally superposed, and generic indefinite-causal-order strategies.
  arXiv  Detail & Related papers  (2024-09-11T07:36:40Z)
• Last-Iterate Global Convergence of Policy Gradients for Constrained Reinforcement Learning [62.81324245896717]
  We introduce an exploration-agnostic algorithm, called C-PG, which exhibits global last-ite convergence guarantees under (weak) gradient domination assumptions. We numerically validate our algorithms on constrained control problems, and compare them with state-of-the-art baselines.
  arXiv  Detail & Related papers  (2024-07-15T14:54:57Z)
• A Provably Efficient Option-Based Algorithm for both High-Level and Low-Level Learning [54.20447310988282]
  We present a meta-algorithm alternating between regret minimization algorithms instanced at different (high and low) temporal abstractions. At the higher level, we treat the problem as a Semi-Markov Decision Process (SMDP), with fixed low-level policies, while at a lower level, inner option policies are learned with a fixed high-level policy.
  arXiv  Detail & Related papers  (2024-06-21T13:17:33Z)
• Ensembling Portfolio Strategies for Long-Term Investments: A Distribution-Free Preference Framework for Decision-Making and Algorithms [0.0]
  This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. We introduce a novel framework for decision-making in combining strategies, irrespective of market conditions. We show results in favor of the proposed strategies, albeit with small tradeoffs in their Sharpe ratios.
  arXiv  Detail & Related papers  (2024-06-05T23:08:57Z)
• StrategyLLM: Large Language Models as Strategy Generators, Executors, Optimizers, and Evaluators for Problem Solving [76.5322280307861]
  StrategyLLM allows LLMs to perform inductive reasoning, deriving general strategies from specific task instances, and deductive reasoning, applying these general strategies to particular task examples, for constructing generalizable and consistent few-shot prompts. Experimental results demonstrate that StrategyLLM outperforms the competitive baseline CoT-SC that requires human-annotated solutions on 13 datasets across 4 challenging tasks without human involvement, including math reasoning (34.2% $rightarrow$ 38.8%), commonsense reasoning (70.3% $rightarrow$ 72.5%), algorithmic reasoning (73.7% $rightarrow$ 85.0
  arXiv  Detail & Related papers  (2023-11-15T09:18:09Z)
• Risk-reducing design and operations toolkit: 90 strategies for managing risk and uncertainty in decision problems [65.268245109828]
  This paper develops a catalog of such strategies and develops a framework for them. It argues that they provide an efficient response to decision problems that are seemingly intractable due to high uncertainty. It then proposes a framework to incorporate them into decision theory using multi-objective optimization.
  arXiv  Detail & Related papers  (2023-09-06T16:14:32Z)
• Tight Cram\'{e}r-Rao type bounds for multiparameter quantum metrology through conic programming [61.98670278625053]
  It is paramount to have practical measurement strategies that can estimate incompatible parameters with best precisions possible. Here, we give a concrete way to find uncorrelated measurement strategies with optimal precisions. We show numerically that there is a strict gap between the previous efficiently computable bounds and the ultimate precision bound.
  arXiv  Detail & Related papers  (2022-09-12T13:06:48Z)
• A Globally Convergent Evolutionary Strategy for Stochastic Constrained Optimization with Applications to Reinforcement Learning [0.6445605125467573]
  Evolutionary strategies have been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. Convergence guarantees for evolutionary strategies to optimize constrained problems are however lacking in the literature.
  arXiv  Detail & Related papers  (2022-02-21T17:04:51Z)
• Quantum process discrimination with restricted strategies [2.030567625639093]
  We present a general formulation of the task of finding the maximum success probability for discriminating quantum processes. We derive necessary and sufficient conditions for an optimal restricted strategy to be optimal within the set of all strategies. This finding has the potential to provide a deeper insight into the discrimination performance of various restricted strategies.
  arXiv  Detail & Related papers  (2021-04-19T04:02:51Z)
• Mixed Strategies for Robust Optimization of Unknown Objectives [93.8672371143881]
  We consider robust optimization problems, where the goal is to optimize an unknown objective function against the worst-case realization of an uncertain parameter. We design a novel sample-efficient algorithm GP-MRO, which sequentially learns about the unknown objective from noisy point evaluations. GP-MRO seeks to discover a robust and randomized mixed strategy, that maximizes the worst-case expected objective value.
  arXiv  Detail & Related papers  (2020-02-28T09:28:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.