Generalizable control for multiparameter quantum metrology

• URL: http://arxiv.org/abs/2012.13377v2
• Date: Thu, 29 Apr 2021 16:10:12 GMT
• Title: Generalizable control for multiparameter quantum metrology
• Authors: Han Xu, Lingna Wang, Haidong Yuan, Xin Wang
• Abstract summary: We study the generalizability of optimal control, namely, optimal controls that can be systematically updated across a range of parameters with minimal cost. We argue that the generalization of reinforcement learning is through a mechanism similar to the analytical scheme.
• Score: 20.506414877440644
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum control can be employed in quantum metrology to improve the precision limit for the estimation of unknown parameters. The optimal control, however, typically depends on the actual values of the parameters and thus needs to be designed adaptively with the updated estimations of those parameters. Traditional methods, such as gradient ascent pulse engineering (GRAPE), need to be rerun for each new set of parameters encountered, making the optimization costly, especially when many parameters are involved. Here we study the generalizability of optimal control, namely, optimal controls that can be systematically updated across a range of parameters with minimal cost. In cases where control channels can completely reverse the shift in the Hamiltonian due to a change in parameters, we provide an analytical method which efficiently generates optimal controls for any parameter starting from an initial optimal control found by either GRAPE or reinforcement learning. When the control channels are restricted, the analytical scheme is invalid, but reinforcement learning still retains a level of generalizability, albeit in a narrower range. In cases where the shift in the Hamiltonian is impossible to decompose to available control channels, no generalizability is found for either the reinforcement learning or the analytical scheme. We argue that the generalization of reinforcement learning is through a mechanism similar to the analytical scheme. Our results provide insights into when and how the optimal control in multiparameter quantum metrology can be generalized, thereby facilitating efficient implementation of optimal quantum estimation of multiple parameters, particularly for an ensemble of systems with ranges of parameters.

Related papers

• Scaling Exponents Across Parameterizations and Optimizers [94.54718325264218]
  We propose a new perspective on parameterization by investigating a key assumption in prior work. Our empirical investigation includes tens of thousands of models trained with all combinations of threes. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work.
  arXiv  Detail & Related papers  (2024-07-08T12:32:51Z)
• Quantum control by the environment: Turing uncomputability, Optimization over Stiefel manifolds, Reachable sets, and Incoherent GRAPE [56.47577824219207]
  In many practical situations, the controlled quantum systems are open, interacting with the environment. In this note, we briefly review some results on control of open quantum systems using environment as a resource.
  arXiv  Detail & Related papers  (2024-03-20T10:09:13Z)
• A Unified Gaussian Process for Branching and Nested Hyperparameter Optimization [19.351804144005744]
  In deep learning, tuning parameters with conditional dependence are common in practice. New GP model accounts for the dependent structure among input variables through a new kernel function. High prediction accuracy and better optimization efficiency are observed in a series of synthetic simulations and real data applications of neural networks.
  arXiv  Detail & Related papers  (2024-01-19T21:11:32Z)
• Optimal Control Strategies for Parameter Estimation of Quantum Systems [0.0]
  We describe the similarities, differences, and advantages of two approaches to optimal control theory. We show that the control mechanisms are generally equivalent, except when the decoherence is not negligible. In this latter case, the precision achieved with selective controls can be several orders of magnitude better than that given by the QFI.
  arXiv  Detail & Related papers  (2023-06-19T07:09:05Z)
• Optimal protocols for quantum metrology with noisy measurements [0.0]
  We show that a quantum preprocessing-optimized parameter determines the ultimate precision limit for quantum sensors under measurement noise. Applications to noisy quantum states and thermometry are presented, as well as explicit circuit constructions of optimal controls.
  arXiv  Detail & Related papers  (2022-10-20T16:37:47Z)
• Optimal control for Hamiltonian parameter estimation in non-commuting and bipartite quantum dynamics [0.0]
  We extend optimally controlled estimation schemes for single qubits to non-commuting dynamics as well as two interacting qubits. These schemes demonstrate improvements in terms of maximal precision, time-stability, as well as robustness over uncontrolled protocols.
  arXiv  Detail & Related papers  (2022-05-05T04:10:17Z)
• Sparsity in Partially Controllable Linear Systems [56.142264865866636]
  We study partially controllable linear dynamical systems specified by an underlying sparsity pattern. Our results characterize those state variables which are irrelevant for optimal control.
  arXiv  Detail & Related papers  (2021-10-12T16:41:47Z)
• Direct Optimal Control Approach to Laser-Driven Quantum Particle Dynamics [77.34726150561087]
  We propose direct optimal control as a robust and flexible alternative to indirect control theory. The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential.
  arXiv  Detail & Related papers  (2020-10-08T07:59:29Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• Online Parameter Estimation for Safety-Critical Systems with Gaussian Processes [6.122161391301866]
  We present a Bayesian optimization framework based on Gaussian processes (GPs) for online parameter estimation. It uses an efficient search strategy over a response surface in the parameter space for finding the global optima with minimal function evaluations. We demonstrate our technique on an actuated planar pendulum and safety-critical quadrotor in simulation with changing parameters.
  arXiv  Detail & Related papers  (2020-02-18T20:38:00Z)
• Time-local optimal control for parameter estimation in the Gaussian regime [68.8204255655161]
  instantaneous control unitaries may be used to mitigate the decrease of information caused by an open dynamics. A possible, locally optimal (in time) choice for such controls is the one that maximises the time-derivative of the quantum Fisher information.
  arXiv  Detail & Related papers  (2020-01-10T16:24:31Z)

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.