Quantum Hamiltonian and dipole moment identification   in presence of large control perturbations

Fu, Ying; Turinici, Gabriel

doi:10.1051/cocv/2016026

Cited by 8 publications

(9 citation statements)

References 21 publications

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“…Reasoning as in the proof of theorem 4.1 of [7], this implies that there exists W ∈ SU (N ) diagonal such that y κ O ( ) µ 2 = W y µ 1 W −1 . Since at least one of Y 1 or Y 2 is non-null, we can suppose, without loss of generality, that y = 0; we deduce the existence of some λ ∈ R \ {0}…”

Section: Hyp-mentioning

confidence: 89%

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Hamiltonian identification in presence of large control field perturbations

Fu¹,

Rabitz²,

Turinici³

2016

J. Phys. A: Math. Theor.

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Quantum system inversion concerns learning the characteristics of the underlying Hamiltonian by measuring suitable observables from the responses of the system's interaction with members of a set of applied fields. Various aspects of inversion have been confirmed in theoretical, numerical and experimental works. Nevertheless, the presence of noise arising from the applied fields may contaminate the quality of the results. In this circumstance, the observables satisfy probability distributions, but often the noise statistics are unknown. Based on a proposed theoretical framework, we present a procedure to recover both the unknown parts of the Hamiltonian and the unknown noise distribution. The procedure is implemented numerically and seen to perform well for illustrative Gaussian, exponential and bi-modal noise distributions.

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Section: Hyp-mentioning

confidence: 89%

“…The hypothesis Hyp-A is required for identification while Hyp-B is rather a convention. Hypothesis Hyp-C can be relaxed (as in [7]) if the O is a Complete Set of Commuting Observables (CSCO).…”

Section: Hyp-mentioning

confidence: 99%

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Hamiltonian identification in presence of large control field perturbations

Fu¹,

Rabitz²,

Turinici³

2016

J. Phys. A: Math. Theor.

Self Cite

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show abstract

“…In the context of quantum systems, the problem of identifying unknown parameters (or functions) has been explored by a large number of studies and for a variety of applications ranging from molecular physics [12,13,14] and magnetic resonance [15,16,17,18] to quantum information science [19,20,21,22,23,24,25,26,27,28,29] and open quantum systems [30,31,32,33]. Some mathematical results have also been established in this direction [34,35,36,37,38,39,40,41,42]. On the basis of different measurement processes and specific control protocols, the goal of these works is generally to estimate the value of one or several parameters of the system Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

A greedy reconstruction algorithm for the identification of spin distribution

Buchwald,

Ciaramella,

Salomon

et al. 2021

Preprint

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We propose a greedy reconstruction algorithm to find the probability distribution of a parameter characterizing an inhomogeneous spin ensemble. 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 in different examples. A systematic comparison with respect to random constant pulses is done.

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“…Even though the overall literature about Hamiltonian identification problems is quite extensive, the mathematical contribution to this area is rather limited. Important mathematical theoretical contributions can be found in [3,2] and in [12,7], where uniqueness results for quantum inverse problems are proved by exploiting controllability arguments. Other techniques, based on the so-called Carleman's estimate, are used in [2] to deduce uniqueness results for inverse problems governed by Schrödinger-type equations in presence of discontinuous coefficients.…”

mentioning

confidence: 99%

Analysis of a greedy reconstruction algorithm

Buchwald¹,

Ciaramella²,

Salomon³

2020

Preprint

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A novel and detailed convergence analysis is presented for a greedy algorithm that was introduced in [13] for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition of the reconstruction process and on an ansatz for the unknown operator obtained by an a priori chosen set of linearly independent matrices. The presented convergence analysis focuses on linear-quadratic (optimization) problems governed by linear differential systems and reveals the strong dependence of the performance of the greedy algorithm on the observability properties of the system and on the ansatz of the basis elements. Moreover, the analysis allows us to use a precise (and in some sense optimal) choice of basis elements for the linear case and led to the introduction of a new and more robust optimized greedy reconstruction algorithm. This optimized approach also applies to nonlinear Hamiltonian reconstruction problems, and its efficiency is demonstrated by numerical experiments.

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Quantum Hamiltonian and dipole moment identification in presence of large control perturbations

Cited by 8 publications

References 21 publications

Hamiltonian identification in presence of large control field perturbations

Hamiltonian identification in presence of large control field perturbations

A greedy reconstruction algorithm for the identification of spin distribution

Analysis of a greedy reconstruction algorithm

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