Quantum control papers on arXiv, selected and classified automatically by QOC. https://llorebaga.github.io/QOC/topics/krotov/ 2026-07-25T00:00:00Z QOC https://arxiv.org/abs/2607.23276 2026-07-25T00:00:00Z 2026-07-25T00:00:00Z Martín D. JiménezMurilo D. ForlevesiEmanuel F. de LimaLeonardo K. Castelano

Achieving scalable quantum computing demands high-fidelity operations capable of mitigating population leakage into non-computational states. Physics-Informed Neural Networks (PINNs) have recently emerged as a powerful paradigm to unify quantum hardware characterization (inverse problems) and pulse engineering (direct problems), laying the foundational architecture for autonomous quantum processors. However, standard PINN frameworks face severe numerical bottlenecks, such as spectral bias, when attempting to simultaneously solve highly oscillatory multi-level dynamics and optimize continuous control fields under strict global phase constraints. In this work, we propose an enhanced PINN scheme for quantum optimal control (PINNQOC) that circumvents these limitations by incorporating Fourier feature embeddings, dynamic epoch normalization, and an informed pre-training routine. To rigorously evaluate its performance, we systematically benchmark our framework against two premier continuous control solvers: the first-order Krotov method and the second-order Projection Operator Newton Method for Trajectory Optimization (PRONTO). These techniques are applied to implement multiple quantum gates on a truncated three-level fluxonium qubit and a four-level Nitrogen-Vacancy center coupled to a Carbon-13 nuclear spin. Our advanced PINNQOC approach successfully suppresses population leakage while achieving gate fidelities exceeding 99.9$\%$, matching the efficacy of traditional solvers. Finally, we provide a comprehensive analysis of computational times, iteration efficiency, and mean leakage, highlighting the distinct trade-offs and avenues for embedding physics-guided machine learning into automated quantum hardware pipelines.

https://arxiv.org/abs/2606.22212 2026-06-20T00:00:00Z 2026-09-21T00:00:00Z Denis JankovićSaba TaherpourPaul-Louis EtienneyPaul-Antoine HervieuxChristoph Wolf

A central goal of quantum optimal control is to achieve high-fidelity and low-energy control pulses. When quantum optimal control methods optimize every point of a pulse discretized over small time steps independently this can yield high fidelity control but also results in broadband and energy-hungry waveforms. We extend MAGICARP, a shooting method inspired by Pontryagin's maximum principle on energy that generates an entire pulse from a small set of parameters, making it smooth and energy-efficient by construction, from driftless systems to closed systems with the constant drift Hamiltonian of two exchange-coupled spins in an external magnetic field. The optimization proceeds in stages: the dressed states of the drift Hamiltonian structure the target, an initial shooting optimization is performed in the rotating-wave frame, and an exact laboratory-frame refinement follows. Benchmarked against Krotov and GRAPE at matched gate infidelity, MAGICARP consistently achieves the lowest energy and a conserved pulse area, concentrates its spectral weight on the gate-relevant transitions, and is the most robust to fluctuations in the exchange coupling; GRAPE independently converges to essentially the same pulse while black-box Krotov meets the same error at an order-of-magnitude energy premium. This method-independence is what qualifies the bounded solver as a measurement instrument, and the central result follows: a large statistical survey of unselected optimization runs resolves a weak-driving quantum speed limit for two exchange-coupled electron spins: low-amplitude realizations of the two-qubit quantum Fourier transform cease to exist below a critical gate time, and the minimum control energy diverges on approach to this limit. The divergence obeys a simple two-parameter area--pole law, $E_2^{\mathrm{law}}(T)=A/T+B/(T-T^*)$.

https://arxiv.org/abs/2603.11697 2026-03-12T00:00:00Z 2026-03-12T00:00:00Z Boris WembeUsman AliTorsten MeierSina Ober-Blöbaum

This paper presents a class of structure-preserving numerical methods for quantum optimal control problems, based on commutator-free Cayley integrators. Starting from the Krotov framework, we reformulate the forward and backward propagation steps using Cayley-type schemes that preserve unitarity and symmetry at the discrete level. This approach eliminates the need for matrix exponentials and commutators, leading to significant computational savings while maintaining higher-order accuracy. We first recall the standard linear setting and then extend the formulation to nonlinear Schrödinger and Gross-Pitaevskii equations using a Cayley-polynomial interpolation strategy. Numerical experiments on state-transfer problems illustrate that the CF-Cayley method achieves the same accuracy as high-order exponential or Cayley-Magnus schemes at substantially lower cost, especially for longtime or highly oscillatory dynamics. In the nonlinear regime, the structure-preserving properties of the method ensure stability and norm conservation, making it a robust tool for large-scale quantum control simulations. The proposed framework thus bridges geometric integration and optimal control, offering an efficient and reliable alternative to existing exponential-based propagators.

https://arxiv.org/abs/2511.00323 2025-10-31T00:00:00Z 2025-12-09T00:00:00Z Da-Wei LuoEdward YuTing Yu

We considered the transfer of continuous-variable entangled states in coupled oscillator chains embedded in a generic environment. We demonstrate high-fidelity transfer via optimal control in two configurations - a linear chain and an X-shaped chain. More specifically, we use the Krotov optimization algorithm to design control fields that achieve the desired state transfer. Under the environmental memory effects, the Krotov algorithm needs to be modified, since the dissipative terms in non-Markovian dynamics are generally governed by the time-dependent system Hamiltonian. Remarkably, we can achieve high-fidelity transfer by simply tuning the frequencies of the oscillators while keeping the coupling strength constant, even in the presence of open-system effects. For the system under consideration, we find that quantum memory effects can aid in the transfer of entanglement and show improvement over the memoryless case. In addition, it is possible to target a range of entangled states, making it unnecessary to know the parameters of the initial state beforehand.

https://arxiv.org/abs/2507.12448 2025-07-16T00:00:00Z 2025-10-15T00:00:00Z Jiahao WuGuanjie HeWenyuan ZhuoQuan FuXin Wang

Exchange-only (EO) qubits, implemented in triple-quantum-dot systems, offer a compelling platform for scalable semiconductor-based quantum computing by enabling universal control through purely exchange interactions. While high-fidelity single- and two-qubit gates have been demonstrated, the synthesis of efficient multi-qubit operations-such as the Toffoli gate-remains a key bottleneck. Conventional gate decompositions into elementary operations lead to prohibitively long and error-prone pulse sequences, limiting practical deployment. In this work, we introduce a gradient-based optimization algorithm, Jenga-Krotov (JK), tailored to discover compact, high-fidelity EO gate sequences. Applying JK to the Toffoli gate, we reduce the number of required exchange unitaries from 216 (in direct decomposition) to 92, and compress the time steps required from 162 to 50, all while maintaining target fidelity. Under realistic noise, the accumulated gate error from our optimized sequence is an order of magnitude lower than that of conventional approaches. We have also applied the JK algorithm to other multi-qubit gates and algorithm. For the Fredkin gate, it reduces the number of time steps from 200 to 104 and the number of exchange unitaries from 276 to 172. For the quantum Fourier transform, it compresses the sequence from 180 to 80 time steps and from 237 to 202 exchange unitaries. These results demonstrate that the JK algorithm is a general and scalable strategy for multi-qubit gate synthesis in EO architectures, potentially facilitating realization of multi-qubit algorithms on semiconductor platforms.

https://arxiv.org/abs/2404.16227 2024-04-24T00:00:00Z 2025-02-13T00:00:00Z Pengju ChenDa-Wei LuoTing Yu

We investigated the optimal control of a continuous variable system, focusing on entanglement generation in an optomechanical system without utilizing Fock basis cutoffs. Using the Krotov algorithm to optimize the dynamics of the covariance matrix, we illustrated how to design a control objective function to manipulate the dynamics of the system to generate a desirable target state. We showed that entanglement between the macroscopic mechanical mirror and the quantum optical cavity can be reliably generated through imposing the control on the detuning of the external laser field. It has be shown that the control may be still achieved when imposing spectral constraints on the external field to restrict it to low-frequency components. In addition, we systematically studies the effects of quantum control on non-Markovian open system dynamics. We observed that memory effects can play a beneficial role in mitigating the detrimental impact of environmental noises. Specifically, the entanglement generated shows reduced decay in the presence of these memory effects.

https://arxiv.org/abs/2308.06119 2023-08-11T00:00:00Z 2023-08-11T00:00:00Z Oleg V. MorzhinAlexander Pechen

This work considers two-qubit open quantum systems driven by coherent and incoherent controls. Incoherent control induces time-dependent decoherence rates via time-dependent spectral density of the environment which is used as a resource for controlling the system. The system evolves according to the Gorini-Kossakowski-Sudarshan-Lindblad master equation with time-dependent coefficients. For two types of interaction with coherent control, three types of objectives are considered: 1) maximizing the Hilbert-Schmidt overlap between the final and target density matrices; 2) minimizing the Hilbert-Schmidt distance between these matrices; 3) steering the overlap to a given value. For the first problem, we develop the Krotov type methods directly in terms of density matrices with or without regularization for piecewise continuous constrained controls and find the cases where the methods produce (either exactly or with some precision) zero controls which satisfy the Pontryagin maximum principle and produce the overlap's values close to their upper estimates. For the problems 2) and 3), we find cases when the dual annealing method steers the objectives close to zero and produces a non-zero control.

https://arxiv.org/abs/2208.03114 2022-08-05T00:00:00Z 2023-07-25T00:00:00Z Marllos E. FonsecaFelipe F. FanchiniEmanuel F. de LimaLeonardo K. Castelano

We apply the Krotov method for open and closed quantum systems with the objective of finding optimized controls to manipulate qubit/qutrit systems in the presence of the external environment. In the case of unitary optimization, the Krotov method is first applied to a quantum system neglecting its interaction with the environment. The resulting controls from the unitary optimization are then used to drive the system along with the environmental noise. In the case of non-unitary optimization, the Krotov method already takes into account the noise during the optimization process. We consider two distinct computational task: target-state preparation and quantum gate implementation. These tasks are carried out in simple qubit/qutrit systems and also in systems presenting leakage states. For the state-preparation cases, the controls from the non-unitary optimization outperform the controls from the unitary optimization. However, as we show here, this is not always true for the implementation of quantum gates. There are some situations where the unitary optimization performs equally well compared to the non-unitary optimization. We verify that these situations corresponds to either the absence of leakage states or to the effects of dissipation being spread uniformly over the system, including non-computational levels. For such cases, the quantum gate implementation must cover the entire Hilbert space and there is no way to dodge dissipation. On the other hand, if the subspace containing the computational levels and its complement are differently affected by dissipation, the non-unitary optimization becomes effective.

https://arxiv.org/abs/2006.16817 2020-06-29T00:00:00Z 2020-07-08T00:00:00Z Tejas Shetty

A great number of quantum control papers have used one of the variants of the monotonically convergent variational control algorithm of Krotov (as described in Maday and Turinici (2003), Tannor et al. (1992), Zhu and Rabitz (1998), etc). The paper "Speeding up Thermalisation via Open Quantum System Variational Optimisation" by N, Suri, et al. [EPJST 227, 203 -216 (2018), arXiv:1711.08776] provides us a way of carrying out Krotov algorithm for open quantum systems. We shall prove the Theorem 1 of the paper, greatly expanding upon the brief treatment given in appendix 1 of the same.

https://arxiv.org/abs/1904.01008 2019-04-01T00:00:00Z 2019-07-02T00:00:00Z Allan Grønlund

The paper [Sørensen et al., Nature 532] considers how human players compare to algorithms for solving the Quantum Moves game BringHomeWater and design new algorithms based on the intuition extracted from players. The claim by [Sørensen et al., Nature 532] is that players outperform widely used algorithms, in particular the KASS algorithm, based on the Krotov algorithm, and that player intuition is crucial to develop improved methods. However, as initially discussed by D. Sels [D. Sels, Phys. Rev. A 97], a standard Coordinate Ascent algorithm outperforms all players by a large margin. Albeit D. Sels only compare to player solutions, the simple algorithm outperforms all algorithms based on player solutions and Krotov, and it does so using much less time and iterations. In this paper we elaborate on the methods discussed by D. Sels and verify that the presented algorithm, solves the problem better than all players and algorithms derived from player solutions in [Sørensen et al., Nature 532]. We also verify the theoretical analysis presented by D. Sels, that gives a theoretically derived protocol that outperforms all players. We add a comparison with gradient ascent or GRAPE. Starting from uniform random values, GRAPE outperforms all players by a large margin. GRAPE works at least as well as the methods from [Sørensen et al., Nature 532] initialized with player solutions. A standard analysis of the results from GRAPE provides a starting point for GRAPE, that outperform all algorithms from [Sørensen et al., Nature 532]. We compare with a basic Krotov algorithm, and get results similar to GRAPE, clearly outperforming players and the KASS algorithm. These experiments verify and underline the result in [D. Sels, Phys. Rev. A 97] that the conclusions from [Sørensen et al., Nature 532] regarding algorithms are untenable. In fact the opposite conclusions are true.

https://arxiv.org/abs/1902.11284 2019-02-28T00:00:00Z 2019-12-16T00:00:00Z Michael H. GoerzDaniel BasilewitschFernando Gago-EncinasMatthias G. KraussKarl P. HornDaniel M. ReichChristiane P. Koch

We present a new open-source Python package, krotov, implementing the quantum optimal control method of that name. It allows to determine time-dependent external fields for a wide range of quantum control problems, including state-to-state transfer, quantum gate implementation and optimization towards an arbitrary perfect entangler. Krotov's method compares to other gradient-based optimization methods such as gradient-ascent and guarantees monotonic convergence for approximately time-continuous control fields. The user-friendly interface allows for combination with other Python packages, and thus high-level customization. The package is being developed at https://github.com/qucontrol/krotov

https://arxiv.org/abs/1902.02157 2019-02-06T00:00:00Z 2021-05-05T00:00:00Z Xiao-Ming ZhangZezhu WeiRaza AsadXu-Chen YangXin Wang

Reinforcement learning has been widely used in many problems, including quantum control of qubits. However, such problems can, at the same time, be solved by traditional, non-machine-learning methods, such as stochastic gradient descent and Krotov algorithms, and it remains unclear which one is most suitable when the control has specific constraints. In this work, we perform a comparative study on the efficacy of three reinforcement learning algorithms: tabular Q-learning, deep Q-learning, and policy gradient, as well as two non-machine-learning methods: stochastic gradient descent and Krotov algorithms, in the problem of preparing a desired quantum state. We found that overall, the deep Q-learning and policy gradient algorithms outperform others when the problem is discretized, e.g. allowing discrete values of control, and when the problem scales up. The reinforcement learning algorithms can also adaptively reduce the complexity of the control sequences, shortening the operation time and improving the fidelity. Our comparison provides insights into the suitability of reinforcement learning in quantum control problems.

https://arxiv.org/abs/1809.09562 2018-09-25T00:00:00Z 2019-04-30T00:00:00Z Oleg V. MorzhinAlexander Pechen

Mathematical problems of optimal control in quantum systems attract high interest in connection with fundamental questions and existing and prospective applications. An important problem is the development of methods for constructing controls for quantum systems. One of the commonly used methods is the Krotov method initially proposed beyond quantum control in the articles by V.F.~Krotov and I.N.~Feldman (1978, 1983). The method was used to develop a novel approach for finding optimal controls for quantum systems in [D.J. Tannor, V. Kazakov, V. Orlov, In: Time-Dependent Quantum Molecular Dynamics, Boston, Springer, 347--360 (1992)] and [J.~Somlói, V.A.~Kazakov, D.J.~Tannor, Chem. Phys., 172:1, 85--98 (1993)], and in many works of various scientists, as described in details in this review. The review discusses mathematical aspects of this method for optimal control of closed quantum systems. It outlines various modifications with respect to defining the improvement function (which in most cases is linear or linear-quadratic), constraints on control spectrum and on the states of a quantum system, regularizers, etc. The review describes applications of the Krotov method to control of molecular dynamics, manipulation of Bose-Einstein condensate, quantum gate generation. We also discuss comparison with GRAPE (GRadient Ascent Pulse Engineering), CRAB (Chopped Random-Basis), the Zhu---Rabitz and the Maday---Turinici methods.

https://arxiv.org/abs/1409.2976 2014-09-10T00:00:00Z 2014-09-10T00:00:00Z Georg JägerDaniel M. ReichMichael H. GoerzChristiane P. KochUlrich Hohenester

We study optimal quantum control of the dynamics of trapped Bose-Einstein condensates: The targets are to split a condensate, residing initially in a single well, into a double well, without inducing excitation; and to excite a condensate from the ground to the first excited state of a single well. The condensate is described in the mean-field approximation of the Gross-Pitaevskii equation. We compare two optimization approaches in terms of their performance and ease of use, namely gradient ascent pulse engineering (GRAPE) and Krotov's method. Both approaches are derived from the variational principle but differ in the way the control is updated, additional costs are accounted for, and second order derivative information can be included. We find that GRAPE produces smoother control fields and works in a black-box manner, whereas Krotov with a suitably chosen step size parameter converges faster but can produce sharp features in the control fields.

https://arxiv.org/abs/1307.3568 2013-07-12T00:00:00Z 2013-07-12T00:00:00Z Daniel M. ReichJose P. PalaoChristiane P. Koch

Shaped pulses obtained by optimal control theory often possess unphysically broad spectra. In principle, the spectral width of a pulse can be restricted by an additional constraint in the optimization functional. However, it has so far been impossible to impose spectral constraints while strictly guaranteeing monotonic convergence. Here, we show that Krotov's method allows for simultaneously imposing temporal and spectral constraints without perturbing monotonic convergence, provided the constraints can be expressed as positive semi-definite quadratic forms. The optimized field is given by an integral equation which can be solved efficiently using the method of degenerate kernels. We demonstrate that Gaussian filters suppress undesired frequency components in the control of non-resonant two-photon absorption.

https://arxiv.org/abs/1304.6500 2013-04-24T00:00:00Z 2013-04-24T00:00:00Z Mamadou NdongMarc LapertChristiane P. KochDominique Sugny

We apply two different monotonically convergent optimization algorithms to the control of molecular rotational dynamics by laser pulses. This example represents a quantum control problem where the interaction of the system with the external field is non-linear. We test the validity and accuracy of the two methods on the key control targets of producing molecular orientation and planar delocalization at zero temperature, and maximizing permanent alignment at non-zero temperature.

https://arxiv.org/abs/1103.5435 2011-03-28T00:00:00Z 2011-03-28T00:00:00Z Sophie SchirmerPierre de Fouquieres

Efficient algorithms for the discovery of optimal control designs for coherent control of quantum processes are of fundamental importance. One important class of algorithms are sequential update algorithms generally attributed to Krotov. Although widely and often successfully used, the associated theory is often involved and leaves many crucial questions unanswered, from the monotonicity and convergence of the algorithm to discretization effects, leading to the introduction of ad-hoc penalty terms and suboptimal update schemes detrimental to the performance of the algorithm. We present a general framework for sequential update algorithms including specific prescriptions for efficient update rules with inexpensive dynamic search length control, taking into account discretization effects and eliminating the need for ad-hoc penalty terms. The latter, while necessary to regularize the problem in the limit of infinite time resolution, i.e., the continuum limit, are shown to be undesirable and unnecessary in the practically relevant case of finite time resolution. Numerical examples show that the ideas underlying many of these results extend even beyond what can be rigorously proved.

https://arxiv.org/abs/1008.5126 2010-08-30T00:00:00Z 2012-03-12T00:00:00Z Daniel M. ReichMamadou NdongChristiane P. Koch

The non-linear optimization method developed by Konnov and Krotov [Automation and Remote Control 60, 1427 (1999)] has been used previously to extend the capabilities of optimal control theory from the linear to the non-linear Schrödinger equation [Sklarz and Tannor, Phys. Rev. A 66, 053619 (2002)]. Here we show that based on the Konnov-Krotov method, monotonically convergent algorithms are obtained for a large class of quantum control problems. It includes, in addition to non-linear equations of motion, control problems that are characterized by non-unitary time evolution, non-linear dependencies of the Hamiltonian on the control, time-dependent targets and optimization functionals that depend to higher than second order on the time-evolving states. We furthermore show that the non-linear (second order) contribution can be estimated either analytically or numerically, yielding readily applicable optimization algorithms. We demonstrate monotonic convergence for an optimization functional that is an eighth-degree polynomial in the states. For the 'standard' quantum control problem of a convex final-time functional, linear equations of motion and linear dependency of the Hamiltonian on the field, the second-order contribution is not required for monotonic convergence but can be used to speed up convergence. We demonstrate this by comparing the performance of first and second order algorithms for two examples.

https://arxiv.org/abs/1002.1539 2010-02-08T00:00:00Z 2010-02-08T00:00:00Z Ivan I. MaximovNiels Chr. NielsenJulien SalomonGabriel Turinici

The past decade has demonstrated increasing interests in using optimal control based methods within coherent quantum controllable systems. The versatility of such methods has been demonstrated with particular elegance within nuclear magnetic resonance (NMR) where natural separation between coherent and dissipative spin dynamics processes has enabled coherent quantum control over long periods of time to shape the experiment to almost ideal adoption to the spin system and external manipulations. This has led to new design principles as well as powerful new experimental methods within magnetic resonance imaging, liquid-state and solid-state NMR spectroscopy. For this development to continue and expand, it is crucially important to constantly improve the underlying numerical algorithms to provide numerical solutions which are optimally compatible with implementation on current instrumentation and at same time are numerically stable and offer fast monotonic convergence towards the target. Addressing such aims, we here present a smoothing monotonically convergent algorithm for pulse sequence design in magnetic resonance which with improved optimization stability lead to smooth pulse sequence easier to implement experimentally and potentially understand within the analytical framework of modern NMR spectroscopy.

https://arxiv.org/abs/0910.5587 2009-10-29T00:00:00Z 2010-09-21T00:00:00Z Tatsuhiko KoikeYosuke Okudaira

We formulate and investigate the simplest version of time-optimal quantum computation theory (t-QCT), where the computation time is defined by the physical one and the Hamiltonian contains only one- and two-qubit interactions. This version of t-QCT is also considered as optimality by sub-Riemannian geodesic length. The work has two aims: one is to develop a t-QCT itself based on physically natural concept of time, and the other is to pursue the possibility of using t-QCT as a tool to estimate the complexity in conventional gate-optimal quantum computation theory (g-QCT). In particular, we investigate to what extent is true the statement: time complexity is polynomial in the number of qubits if and only if so is gate complexity. In the analysis, we relate t-QCT and optimal control theory (OCT) through fidelity-optimal computation theory (f-QCT); f-QCT is equivalent to t-QCT in the limit of unit optimal fidelity, while it is formally similar to OCT. We then develop an efficient numerical scheme for f-QCT by modifying Krotov's method in OCT, which has monotonic convergence property. We implemented the scheme and obtained solutions of f-QCT and of t-QCT for the quantum Fourier transform and a unitary operator that does not have an apparent symmetry. The former has a polynomial gate complexity and the latter is expected to have exponential one because a series of generic unitary operators has a exponential gate complexity. The time complexity for the former is found to be linear in the number of qubits, which is understood naturally by the existence of an upper bound. The time complexity for the latter is exponential. Thus the both targets are examples satisfyng the statement above. The typical characteristics of the optimal Hamiltonians are symmetry under time-reversal and constancy of one-qubit operation, which are mathematically shown to hold in fairly general situations.

https://arxiv.org/abs/0906.1051 2009-06-05T00:00:00Z 2009-06-05T00:00:00Z Marc LapertR. TehiniGabriel TuriniciDominique Sugny

We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field is taken as a linear combination of the control field (computed by the standard algorithm) and the filtered field. The parameter of the linear combination is chosen to respect the monotonic behavior of the algorithm and to be as close to the filtered field as possible. We test the efficiency of this method on molecular alignment. Using band-pass filters, we show how to select particular rotational transitions to reach high alignment efficiency. We also consider spectral constraints corresponding to experimental conditions using pulse shaping techniques. We determine an optimal solution that could be implemented experimentally with this technique.

https://arxiv.org/abs/0905.4867 2009-05-29T00:00:00Z 2009-05-29T00:00:00Z Marc LapertR. TehiniGabriel TuriniciDominique Sugny

We consider the optimal control of quantum systems interacting non-linearly with an electromagnetic field. We propose new monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured by a non-standard choice of the cost which is not quadratic in the field. These algorithms can be constructed for pure and mixed-state quantum systems. The efficiency of the method is shown numerically on molecular orientation with a non-linearity of order 3 in the field. Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well-approximated by pulses that could be implemented experimentally.

https://arxiv.org/abs/0801.3935 2008-01-25T00:00:00Z 2008-01-25T00:00:00Z Caroline GollubMarkus KowalewskiRegina de Vivie-Riedle

We present a modified optimal control scheme based on the Krotov method, which allows for strict limitations on the spectrum of the optimized laser fields, without losing monotonic convergence of the algorithm. The method guarantees a close link to learning loop control experiments and is demonstrated for the challenging control of non-resonant Raman transitions, which are used to implement a set of global quantum gates for molecular vibrational qubits.

https://arxiv.org/abs/quant-ph/0503072 2005-03-07T00:00:00Z 2005-03-07T00:00:00Z Julien Salomon

Many numerical simulations in quantum (bilinear) control use the monotonically convergent algorithms of Krotov (introduced by Tannor), Zhu & Rabitz or the general form of Maday & Turinici. This paper presents an analysis of the limit set of controls provided by these algorithms and a proof of convergence in a particular case.