arXiv subjects

F. C. Langbein

Publications and source records attributed to F. C. Langbein.

14 recordsLinked to original sources

arXiv2026

Fidelity-Based Robustness Margins for Finite-Time Quantum Control

We develop a structure-specific fidelity-threshold robustness margin for finite-dimensional closed quantum systems under piecewise-constant coherent control. A scalar physical parameter may perturb the drift, a control Hamiltonian, or another declared Hamiltonian component across the control horizon. A differential sensitivity bound for trace-amplitude gate fidelity yields a threshold-dependent Lipschitz constant on the connected safe parameter component and hence a certified finite perturbation radius. Recentering this certificate produces an iterative one-dimensional method that takes certified safe steps toward the first fidelity-threshold boundary in either parameter direction. A three-qubit gate-control example shows that these finite margins vary by up to a factor of three across controllers of comparable nominal fidelity and contain structure-dependent information not captured by nominal differential sensitivity alone.

quant-ph↗

arXiv2025

Energy Landscape Shaping for Robust Control of Atoms in Optical Lattices

Robust quantum control is crucial for realizing practical quantum technologies. Energy landscape shaping offers an alternative to conventional dynamic control, providing theoretically enhanced robustness and simplifying implementation for certain applications. This work demonstrates the feasibility of robust energy landscape control in a practical implementation with ultracold atoms. We leverage a digital mirror device (DMD) to shape optical potentials, creating complex energy landscapes. To achieve a desired objective, such as efficient quantum state transfer, we formulate a novel hybrid optimization approach that effectively handles both continuous (laser power) and discrete (DMD pixel activation) control parameters. This approach combines constrained quasi-Newton methods with surrogate models for efficient exploration of the vast parameter space. Furthermore, we introduce a framework for analyzing the robustness of the resulting control schemes against experimental uncertainties. By modeling uncertainties as structured perturbations, we systematically assess controller performance and identify robust solutions. We apply these techniques to maximize spin transfer in a chain of trapped atoms, achieving high-fidelity control while maintaining robustness. Our findings provide insights into the experimental viability of controlled spin transfer in cold atom systems. More broadly, the presented optimization and robustness analysis methods apply to a wide range of quantum control problems, offering a toolkit for designing and evaluating robust controllers in complex experimental settings.

quant-ph↗

arXiv2024

Robust Quantum Control in Closed and Open Systems: Theory and Practice

Robust control of quantum systems is an increasingly relevant field of study amidst the second quantum revolution, but there remains a gap between taming quantum physics and robust control in its modern analytical form that culminated in fundamental performance bounds. With certain exceptions such as quantum optical systems that can be modeled as linear stochastic differential equations, quantum systems are not amenable to linear, time-invariant, measurement-based robust control techniques, and thus novel gap-bridging techniques must be developed. This survey is written for control theorists to provide a review of the current state of quantum control and outline the challenges faced in trying to apply modern robust control to quantum systems. We present issues that arise when applying classical robust control theory to quantum systems, typical methods used by quantum physicists to explore such systems and their robustness, as well as a discussion of open problems to be addressed in the field. We focus on general, practical applications and recent work to enable control researchers to contribute to advancing this burgeoning field.

quant-ph↗

arXiv2024

Robustness of Dynamic Quantum Control: Differential Sensitivity Bound

Dynamic control via optimized, piecewise-constant pulses is a common paradigm for open-loop control to implement quantum gates. While numerous methods exist for the synthesis of such controls, there are many open questions regarding the robustness of the resulting control schemes in the presence of model uncertainty; unlike in classical control, there are generally no analytical guarantees on the control performance with respect to inexact modeling of the system. In this paper a new robustness measure based on the differential sensitivity of the gate fidelity error to parametric (structured) uncertainties is introduced, and bounds on the differential sensitivity to parametric uncertainties are used to establish performance guarantees for optimal controllers for a variety of quantum gate types, system sizes, and control implementations. Specifically, it is shown how a maximum allowable perturbation over a set of Hamiltonian uncertainties that guarantees a given fidelity error, can be reliably computed. This measure of robustness is inversely proportional to the upper bound on the differential sensitivity of the fidelity error evaluated under nominal operating conditions. Finally, the results show that the nominal fidelity error and differential sensitivity upper bound are positively correlated across a wide range of problems and control implementations, suggesting that in the high-fidelity control regime, rather than there being a trade-off between fidelity and robustness, higher nominal gate fidelities are positively correlated with increased robustness of the controls in the presence of parametric uncertainties.

quant-ph↗

arXiv2023

Time Domain Sensitivity of the Tracking Error

A strictly time-domain formulation of the log-sensitivity of the error signal to structured plant uncertainty is presented and analyzed through simple but representative classical and quantum systems. Results demonstrate that across a wide range of physical systems, maximization of performance (minimization of the error signal) asymptotically or at a specific time comes at the cost of increased log-sensitivity, implying a time-domain constraint analogous to the frequency-domain identity $\mathbf{S(s) + T(s) = I}$. While of limited value in classical problems based on asymptotic stabilization or tracking, such a time-domain formulation is valuable in assessing the reduced robustness cost concomitant with high-fidelity quantum control schemes predicated on time-based performance measures.

quant-ph↗

arXiv2023

Analyzing and Unifying Robustness Measures for Excitation Transfer Control in Spin Networks

Recent achievements in quantum control have resulted in advanced techniques for designing controllers for applications in quantum communication, computing, and sensing. However, the susceptibility of such systems to noise and uncertainties necessitates robust controllers that perform effectively under these conditions to realize the full potential of quantum devices. The time-domain log-sensitivity and a recently introduced robustness infidelity measure (RIM) are two means to quantify controller robustness in quantum systems. The former can be found analytically, while the latter requires Monte-Carlo sampling. In this work, the correlation between the log-sensitivity and the RIM for evaluating the robustness of single excitation transfer fidelity in spin chains and rings in the presence of dephasing is investigated. We show that the expected differential sensitivity of the error agrees with the differential sensitivity of the RIM, where the expectation is over the error probability distribution. Statistical analysis also demonstrates that the log-sensitivity and the RIM are linked via the differential sensitivity, and that the differential sensitivity and RIM are highly concordant. This unification of two means (one analytic and one via sampling) to assess controller robustness in a variety of realistic scenarios provides a first step in unifying various tools to model and assess robustness of quantum controllers.

quant-ph↗

arXiv2022

Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations

Development of robust quantum control has been challenging and there are numerous obstacles to applying classical robust control to quantum system including bilinearity, marginal stability, state preparation errors, nonlinear figures of merit. The requirement of marginal stability, while not satisfied for closed quantum systems, can be satisfied for open quantum systems where Lindbladian behavior leads to non-unitary evolution, and allows for nonzero classical stability margins, but it remains difficult to extract physical insight when classical robust control tools are applied to these systems. We consider a straightforward example of the entanglement between two qubits dissipatively coupled to a lossy cavity and analyze it using the classical stability margin and structured perturbations. We attempt, where possible, to extract physical insight from these analyses. Our aim is to highlight where classical robust control can assist in the analysis of quantum systems and identify areas where more work needs to be done to develop specific methods for quantum robust control.

quant-ph↗

arXiv2021

Reinforcement Learning vs. Gradient-Based Optimisation for Robust Energy Landscape Control of Spin-1/2 Quantum Networks

We explore the use of policy gradient methods in reinforcement learning for quantum control via energy landscape shaping of XX-Heisenberg spin chains in a model agnostic fashion. Their performance is compared to finding controllers using gradient-based L-BFGS optimisation with restarts, with full access to an analytical model. Hamiltonian noise and coarse-graining of fidelity measurements are considered. Reinforcement learning is able to tackle challenging, noisy quantum control problems where L-BFGS optimization algorithms struggle to perform well. Robustness analysis under different levels of Hamiltonian noise indicates that controllers found by reinforcement learning appear to be less affected by noise than those found with L-BFGS.

quant-ph↗

arXiv2021

Benchmarking GABA Quantification: A Ground Truth Data Set and Comparative Analysis of TARQUIN, LCModel, jMRUI and Gannet

Many tools exist for the quantification of GABA-edited magnetic resonance spectroscopy (MRS) data. Despite a recent consensus effort by the MRS community, literature comparing them is sparse but indicates a methodological bias. While invivo data sets can ascertain the level of agreement between tools, ground-truth is required to establish accuracy, and investigate the sources of discrepancy. We present a novel approach to benchmarking GABA quantification tools, using several series of phantom experiments with iterated GABA concentration. Each series presents a different set of background metabolites and environmental conditions allowing comparison of not only individual estimates, but the ability of tools to characterise changes in GABA across a range of potential confounds. The methodology of the phantom experiments is presented, as well as characterisation of the data. We also perform an initial comparative analysis of several common MRS quantification tools and in-house code, to illustrate utility of the dataset and the potential bias introduced by different quantification methods. The GABA-to-NAA ratios reported by each tool are compared to the ground-truth, and estimation accuracy is assessed by linear regression of this relationship. While the linearity of GABA-to-NAA gradients is generally captured by all of the tools, a large variation in the slope, offset and environmental stability of the gradient is observed. The primary driver of differences in linear combination modelling is the choice of basis function. However, tools employing a common basis and pre-processing still produce differences on the order of 4%. Less-strictly parametrised fitting approaches appear to improve the robustness of quantification, but accurate modelling of edit efficiency calculations is still necessary to avoid systematic offsets. In general, the level of variation suggests that comparisons across...

physics.med-ph↗

arXiv2019

MRSNet: Metabolite Quantification from Edited Magnetic Resonance Spectra With Convolutional Neural Networks

Quantification of metabolites from magnetic resonance spectra (MRS) has many applications in medicine and psychology, but remains a challenging task despite considerable research efforts. For example, the neurotransmitter $γ$-aminobutyric acid (GABA), present in very low concentration in vivo, regulates inhibitory neurotransmission in the brain and is involved in several processes outside the brain. Reliable quantification is required to determine its role in various physiological and pathological conditions. We present a novel approach to quantification of metabolites from MRS with convolutional neural networks --- MRSNet. MRSNet is trained to perform the multi-class regression problem of identifying relative metabolite concentrations from given input spectra, focusing specifically on the quantification of GABA, which is particularly difficult to resolve. Typically it can only be detected at all using special editing acquisition sequences such as MEGA-PRESS. A large range of network structures, data representations and automatic processing methods are investigated. Results are benchmarked using experimental datasets from test objects of known composition and compared to state-of-the-art quantification methods: LCModel, jMRUI (AQUES, QUEST), TARQUIN, VeSPA and Gannet. The results show that the overall accuracy and precision of metabolite quantification is improved using convolutional neural networks.

eess.IV↗

arXiv2018

Robustness of energy landscape control for spin networks under decoherence

Quantum spin networks form a generic system to describe a range of quantum devices for quantum information processing and sensing applications. Understanding how to control them is essential to achieve devices with practical functionalities. Energy landscape shaping is a novel control paradigm to achieve selective transfer of excitations in a spin network with surprisingly strong robustness towards uncertainties in the Hamiltonians. Here we study the effect of decoherence, specifically generic pure dephasing, on the robustness of these controllers. Results indicate that while the effectiveness of the controllers is reduced by decoherence, certain controllers remain sufficiently effective, indicating potential to find highly effective controllers without exact knowledge of the decoherence processes.

quant-ph↗

arXiv2018

Monte Carlo Simulations of Spin Transport in a Strained Nanoscale InGaAs Field Effect Transistor

Spin-based logic devices could operate at very high speed with very low energy consumption and hold significant promise for quantum information processing and metrology. Here, an in-house developed, experimentally verified, ensemble self-consistent Monte Carlo device simulator with a Bloch equation model using a spin-orbit interaction Hamiltonian accounting for Dresselhaus and Rashba couplings is developed and applied to a spin field effect transistor (spinFET) operating under externally applied voltages on a gate and a drain. In particular, we simulate electron spin transport in a \SI{25}{nm} gate length \chem{In_{0.7}Ga_{0.3}As} metal-oxide-semiconductor field-effect transistor (MOSFET) with a CMOS compatible architecture. We observe non-uniform decay of the net magnetization between the source and gate and a magnetization recovery effect due to spin refocusing induced by a high electric field between the gate and drain. We demonstrate coherent control of the polarization vector of the drain current via the source-drain and gate voltages, and show that the magnetization of the drain current is strain-sensitive and can be increased twofold by strain induced into the channel.

physics.comp-ph↗

arXiv2014

Quantum networks: Anti-core of spin chains

The purpose of this paper is to exhibit a quantum network phenomenon - the anti-core---that goes against the classical network concept of congestion core. Classical networks idealized as infinite, Gromov hyperbolic spaces with least-cost path routing (and subject to a technical condition on the Gromov boundary) have a congestion core, defined as a subnetwork that routing paths have a high probability of visiting. Here, we consider quantum networks, more specifically spin chains, define the so-called maximum excitation transfer probability $p_{\max}(i,j)$ between spin $i$ and spin $j$, and show that the central spin has among all other spins the lowest probability of being excited or transmitting its excitation. The anti-core is singled out by analytical formulas for $p_{\mathrm{max}}(i,j)$, revealing the number theoretic properties of quantum chains. By engineering the chain, we further show that this probability can be made vanishingly small.

math-ph↗

arXiv2009

Quantum System Identification: Hamiltonian Estimation using Spectral and Bayesian Analysis

Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation procedure is proposed and evaluated for a model system where a-priori information about the Hamiltonian's structure is available.

quant-ph↗