A greedy reconstruction algorithm for the identification of spin distribution
arXiv:2108.11745 · doi:10.1103/PhysRevA.104.063112
Abstract
We propose a greedy reconstruction algorithm to find the probability distribution of a parameter characterizing an inhomogeneous spin ensemble in Nuclear Magnetic Resonace. The identification is based on the application of a number of constant control processes during a given time for which the final ensemble magnetization vector is measured. From these experimental data, we show that the identifiability of a piecewise constant approximation of the probability distribution is related to the invertibility of a matrix which depends on the different control protocols applied to the system. The algorithm aims to design specific controls which ensure that this matrix is as far as possible from a singular matrix. Numerical simulations reveal the efficiency of this algorithm on different examples. A systematic comparison with respect to random constant pulses is done.
18 pages, 6 figures
References in corpus (11)
- Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
- Singular extremals for the time-optimal control of dissipative spin 1/2 particles
- Correction of Arbitrary Errors in Population Inversion of Quantum Systems by Universal Composite Pulses
- Integrated tool-set for Control, Calibration and Characterization of quantum devices applied to superconducting qubits
- Hamiltonian identifiability assisted by single-probe measurement
- Identification of open quantum systems from observable time traces
- Two-Qubit Hamiltonian Tomography by Bayesian Analysis of Noisy Data
- Geometrical Formalism for Dynamically Corrected Gates in Multiqubit Systems
- Evolution-free Hamiltonian parameter estimation through Zeeman markers
- Optimizing fingerprinting experiments for parameter identification: Application to spin systems
- Newton algorithm for Hamiltonian characterization in quantum control