Optimal Control for Quantum Metrology via Pontryagin's principle
- URL: http://arxiv.org/abs/2105.06931v1
- Date: Fri, 14 May 2021 16:22:57 GMT
- Title: Optimal Control for Quantum Metrology via Pontryagin's principle
- Authors: Chungwei Lin, Yanting Ma, Dries Sels
- Abstract summary: We apply Pontryagin's Maximum Principle to determine the optimal protocol that maximizes the quantum Fisher information for a given evolution time.
The proposed formalism is generalized to problems with control constraints, and can also be used to maximize the classical Fisher information for a chosen measurement.
- Score: 8.920103626492315
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum metrology comprises a set of techniques and protocols that utilize
quantum features for parameter estimation which can in principle outperform any
procedure based on classical physics. We formulate the quantum metrology in
terms of an optimal control problem and apply Pontryagin's Maximum Principle to
determine the optimal protocol that maximizes the quantum Fisher information
for a given evolution time. As the quantum Fisher information involves a
derivative with respect to the parameter which one wants to estimate, we devise
an augmented dynamical system that explicitly includes gradients of the quantum
Fisher information. The necessary conditions derived from Pontryagin's Maximum
Principle are used to quantify the quality of the numerical solution. The
proposed formalism is generalized to problems with control constraints, and can
also be used to maximize the classical Fisher information for a chosen
measurement.
Related papers
- A Precisão da Metrologia Quântica: Limite de Cramér-Rao, Informação de Fisher e possíveis Aplicações Tecnológicas [0.0]
This paper explores as didactically as possible the fundamental principles of both classical and quantum metrology.
We focus on the Cram'er-Rao Bound and how it defines the maximum precision in parameter estimation.
We discuss how quantum states can surpass classical limits, providing much greater precision.
arXiv Detail & Related papers (2024-11-26T18:01:06Z) - An Application of Pontryagin Neural Networks to Solve Optimal Quantum
Control Problems [1.5469452301122175]
Pontryagin maximum principle has proved to play an important role to achieve the maximum fidelity in an optimum time or energy.
We formulate a control constrained optimal control problem where we aim to minimize time and also energy subjected to a quantum system satisfying the bilinear Schrodinger equation.
We make use of the so-called "qutip" package in python, and the newly developed "tfc" python package.
arXiv Detail & Related papers (2023-02-01T17:48:07Z) - Analyzing Prospects for Quantum Advantage in Topological Data Analysis [35.423446067065576]
We analyze and optimize an improved quantum algorithm for topological data analysis.
We show that super-quadratic quantum speedups are only possible when targeting a multiplicative error approximation.
We argue that quantum circuits with tens of billions of Toffoli can solve seemingly classically intractable instances.
arXiv Detail & Related papers (2022-09-27T17:56:15Z) - An Introduction to Quantum Machine Learning for Engineers [36.18344598412261]
Quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers.
This book provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra.
arXiv Detail & Related papers (2022-05-11T12:10:52Z) - Application of Pontryagin's Maximum Principle to Quantum Metrology in
Dissipative Systems [8.920103626492315]
We look for the optimal control that maximizes quantum Fisher information for "twist and turn" problem.
We find that the optimal control is singular without dissipation but can become unbounded once the quantum decoherence is introduced.
arXiv Detail & Related papers (2022-04-30T00:02:57Z) - A Quantum Optimal Control Problem with State Constrained Preserving
Coherence [68.8204255655161]
We consider a three-level $Lambda$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels.
We formulate the quantum optimal control problem with state constraints where the decoherence level remains within a pre-defined bound.
arXiv Detail & Related papers (2022-03-24T21:31:34Z) - High Fidelity Quantum State Transfer by Pontryagin Maximum Principle [68.8204255655161]
We address the problem of maximizing the fidelity in a quantum state transformation process satisfying the Liouville-von Neumann equation.
By introducing fidelity as the performance index, we aim at maximizing the similarity of the final state density operator with the one of the desired target state.
arXiv Detail & Related papers (2022-03-07T13:27:26Z) - Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems.
Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
arXiv Detail & Related papers (2021-08-30T23:50:05Z) - Stochastic optimal control formalism for an open quantum system [15.076862040458124]
A procedure is developed which allows one to express Pontryagin's maximum principle for dissipative quantum system.
Time-optimal computing controls can be efficiently computed without the density matrix.
arXiv Detail & Related papers (2020-11-06T15:37:51Z) - In and out of equilibrium quantum metrology with mean-field quantum
criticality [68.8204255655161]
We study the influence that collective transition phenomena have on quantum metrological protocols.
The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level.
arXiv Detail & Related papers (2020-01-09T19:20:42Z)
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.