arXiv subjects

Sophie Schirmer

Publications and source records attributed to Sophie Schirmer.

At least 19 recordsLinked to original sources

arXiv2025

Robustness Analysis for Quantum Systems Controlled by Continuous-Time Pulses

Differential sensitivity techniques originally developed to study the robustness of energy landscape controllers are generalized to the important case of closed quantum systems subject to continuously varying controls. Vanishing sensitivity to parameter variation is shown to coincide with perfect fidelity, as was the case for time-invariant controls. Upper bounds on the magnitude of the differential sensitivity to any parameter variation are derived based simply on knowledge of the system Hamiltonian and the maximum size of the control inputs.

quant-ph↗

arXiv2025

Geometric Interpretation of Sensitivity to Structured Uncertainties in Spintronic Networks

We present a geometric model of the differential sensitivity of the fidelity error for state transfer in a spintronic network based on the relationship between a set of matrix operators. We show an explicit dependence of the differential sensitivity on the fidelity (error), and we further demonstrate that this dependence does not require a trade-off between the fidelity and sensitivity. Rather, we prove that for closed systems, ideal performance in the sense of perfect state transfer is both necessary and sufficient for optimal robustness in terms of vanishing sensitivity. We demonstrate the utility of this geometric interpretation of the sensitivity by applying the model to explain the sensitivity versus fidelity error data in two examples.

quant-ph↗

arXiv2024

Sensitivity Bounds for Quantum Control and Time-Domain Performance Guarantees

Control of quantum systems via time-varying external fields optimized to maximize a fidelity measure at a given time is a mainstay in modern quantum control. However, save for specific systems, current analysis techniques for such quantum controllers provide no analytical robustness guarantees. In this letter we provide analytical bounds on the differential sensitivity of the gate fidelity error to structured uncertainties for a closed quantum system controlled by piecewise-constant, optimal control fields. We additionally determine those uncertainty structures that result in this worst-case maximal sensitivity. We then use these differential sensitivity bounds to provide conditions that guarantee performance, quantified by the fidelity error, in the face of parameter uncertainty.

quant-ph↗

arXiv2017

Sensitivity and Robustness of Quantum Spin-1/2 Rings to Parameter Uncertainty

Selective transfer of information between spin-1/2 particles arranged in a ring is achieved by optimizing the transfer fidelity over a readout time window via shaping, externally applied, static bias fields. Such static control fields have properties that clash with the expectations of classical control theory. Previous work has shown that there are cases in which the logarithmic differential sensitivity of the transfer fidelity to uncertainty in coupling strength or spillage of the bias field to adjacent spins is minimized by controllers that produce the best fidelity. Here we expand upon these examples and examine cases of both classical and non-classical behavior of logarithmic sensitivity to parameter uncertainty and robustness as measured by the $μ$ function for quantum systems. In particular we examine these properties in an 11-spin ring with a single uncertainty in coupling strength or a single bias spillage.

quant-ph↗

arXiv2017

Comparison of CPMG and Uhrig Dynamic Decoupling (UDD) for tissue refocusing in MRI

Two different dynamic decoupling strategies, the classic CPMG and the more recently proposed UDD protocol are compared in the context of magnetic resonance imaging (MRI). Both sequences were implemented on a 3T human MRI system and relaxometry was performed for a variety of tissue-mimicking agar and agarose gels. We find that CPMG provides moderately better decoupling than \UDD. The results are consistent with experimental noise spectra obtained from \textit{in vivo} spectroscopy results, which suggest that the type of noise spectra obtained would favor \CPMG. Theoretical coherence pathway analysis further suggests that \UDD\ is more susceptible to systematic errors due to static magnetic and radio-frequency field inhomogeneity or imperfect excitation and refocusing pulse profiles.

physics.med-ph↗

arXiv2016

Multi-fractal Geometry of Finite Networks of Spins

Quantum spin networks overcome the challenges of traditional charge-based electronics by encoding the information into spin degrees of freedom. Although beneficial for transmitting information with minimal losses when compared to their charge-based counterparts, the mathematical formalization of the information propagation in a spin(tronic) network is challenging due to its complicated scaling properties. In this paper, we propose a geometric approach---specific to finite networks---for unraveling the information-theoretic phenomena of spin chains and rings by abstracting them as weighted graphs, where the vertices correspond to the spin excitation states and the edges represent the information theoretic distance between pair of nodes. The weighted graph representation of the quantum spin network dynamics exhibits a complex self-similar structure (where subgraphs repeat to some extent over various space scales). To quantify this complex behavior, we develop a new box counting inspired algorithm which assesses the mono-fractal versus multi-fractal properties of quantum spin networks. Besides specific to finite networks, multi-fractality is further compounded by "engineering" or "biasing" the network for selective transfer, as selectivity makes the network more heterogeneous. To demonstrate criticality in finite size systems, we define a thermodynamics inspired framework for describing information propagation and show evidence that some spin chains and rings exhibit an informational phase transition phenomenon, akin to the metal-to-insulator phase transition in Anderson localization in finite media.}

quant-ph↗

arXiv2016

Backaction driven, robust, steady-state long-distance qubit entanglement over lossy channels

We present a scheme for generating robust and persistent entanglement between qubits that do not interact and that are separated by a long and lossy transmission channel, using Markovian reservoir engineering. The proposal uses only the correlated decay into the common channel of remotely separated, driven single-photon qubit transitions. This simple scheme is generic and applicable to various experimental implementations, including circuit and cavity QED, with little experimental overhead compared with methods requiring dynamic control, initialization, measurement, or feedback. In addition to avoiding these inefficiencies, the simple protocol is highly robust against noise, miscalibration, and loss in the channel. We find high quality solutions over a wide range of parameters and show that the optimal strategy reflects a transition from ballistic to diffusive photon transmission, going from symmetrically and coherently driving a common steady state to asymmetrically absorbing photons that are emitted from one qubit by the second. Detailed analysis of the role of the transmission channel shows that allowing bi-directional decay drastically increases indistinguishability and thereby quadratically suppresses infidelity.

quant-ph↗

arXiv2015

Information Transfer Fidelity in Spin Networks and Ring-based Quantum Routers

Spin networks are endowed with an Information Transfer Fidelity (ITF), which defines an absolute upper bound on the probability of transmission of an excitation from one spin to another. The ITF is easily computable but the bound can be reached asymptotically in time only under certain conditions. General conditions for attainability of the bound are established and the process of achiev-ing the maximum transfer probability is given a dynamical model, the translation on the torus. The time to reach the maximum probability is estimated using the simultaneous Diophantine approximation, implemented using a variant of the Lenstra-Lenstra-Lovasz (LLL) algorithm. For a ring with uniform couplings, the network can be made a metric space by defining a distance (satisfying the triangle inequality) that quantifies the lack of transmission fidelity between two nodes. It is shown that transfer fidelities and transfer times can be improved significantly by means of simple controls taking the form of non-dynamic, spatially localized bias fields, opening up the possibility for intelligent design of spin networks and dynamic routing of information encoded in them, while being more flexible than engineering fixed couplings to favor some transfers, and less demanding than control schemes requiring fast dynamic controls.

quant-ph↗

arXiv2015

Time optimal information transfer in spintronics networks

Propagation of information encoded in spin degrees of freedom through networks of coupled spins enables important applications in spintronics and quantum information processing. We study control of information propagation in networks of spin-$\tfrac{1}{2}$ particles with uniform nearest neighbour couplings forming a ring with a single excitation in the network as simple prototype of a router for spin-based information. Specifically optimising spatially distributed potentials, which remain constant during information transfer, simplifies the implementation of the routing scheme. However, the limited degrees of freedom makes finding a control that maximises the transfer probability in a short time difficult. We show that the structure of the eigenvalues and eigenvectors must fulfill a specific condition to be able to maximise the transfer fidelity, and demonstrate that a specific choice among the many potential structures that fulfill this condition significantly improves the solutions found by optimal control.

quant-ph↗

arXiv2015

Training Schrödinger's cat: quantum optimal control

It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a system from a given initial state into a desired target state with minimized expenditure of energy and resources -- as famously applied in the Apollo programme. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantum-enhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. --- Here state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium uniting expertise in optimal control theory and applications to spectroscopy, imaging, quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap to future developments.

quant-ph↗

arXiv2014

Model discrimination for dephasing two-level systems

The problem of model discriminability and parameter identifiability for dephasing two-level systems subject to Hamiltonian control is studied. Analytic solutions of the Bloch equations are used to derive explicit expressions for observables as functions of time for different models. This information is used to give criteria for model discrimination and parameter estimation based on simple experimental paradigms.

quant-ph↗

arXiv2014

The ubiquitous problem of learning system parameters for dissipative two-level quantum systems: Fourier analysis versus Bayesian estimation

We compare the accuracy, precision and reliability of different methods for estimating key system parameters for two-level systems subject to Hamiltonian evolution and decoherence. It is demonstrated that the use of Bayesian modelling and maximum likelihood estimation is superior to common techniques based on Fourier analysis. Even for simple two-parameter estimation problems, the Bayesian approach yields higher accuracy and precision for the parameter estimates obtained. It requires less data, is more flexible in dealing with different model systems, can deal better with uncertainty in initial conditions and measurements, and enables adaptive refinement of the estimates. The comparison results shows that this holds for measurements of large ensembles of spins and atoms limited by Gaussian noise as well as projection noise limited data from repeated single-shot measurements of a single quantum device.

quant-ph↗

arXiv2014

Evolutionary Algorithms for Hard Quantum Control

Although quantum control typically relies on greedy (local) optimization, traps (irregular critical points) in the control landscape can make optimization hard by foiling local search strategies. We demonstrate the failure of greedy algorithms to realize two fast quantum computing gates: a qutrit phase gate and a controlled-not gate. Then we show that our evolutionary algorithm circumvents the trap to deliver effective quantum control in both instances. Even when greedy algorithms succeed, our evolutionary algorithm delivers a superior control procedure because less time resolution is required for the control sequence.

quant-ph↗

arXiv2014

Curvature of quantum rings

We develop a geometric approach to spin networks with Heisenberg or XX coupling. Geometry is acquired by defining a distance on the discrete set of spins. The key feature of the geometry of such networks is their Gauss curvature $κ$, viewed here as the ability to isometrically embed the chain in the standard Riemannian manifold of curvature $κ$. Here we focus on spin rings. Even though their visual geometry is trivial, it turns out that the geometry they acquire from the quantum mechanical distance is far from trivial.

math-ph↗

arXiv2014

Characterization and Control of Quantum Spin Chains and Rings

Information flow in quantum spin networks is considered. Two types of control -- temporal bang-bang switching control and control by varying spatial degrees of freedom -- are explored and shown to be effective in speeding up information transfer and increasing transfer fidelities. The control is model-based and therefore relies on accurate knowledge of the system parameters. An efficient protocol for simultaneous identification of the coupling strength and the exact number of spins in a chain is presented.

quant-ph↗

arXiv2012

Robust quantum gates for systems subject to decoherence via optimal control: Markovian vs non-Markovian dynamics

We study the implementation of one-, two-, and three-qubit quantum gates for interacting qubits using optimal control. Different Markovian and non-Markovian environments are compared and efficient optimisation algorithms utilising analytic gradient expressions and quasi-Newton updates are given for both cases. The performance of the algorithms is analysed for a large set of problems in terms of the fidelities attained and the observed convergence behaviour. New notions of success rate and success speed are introduced and density plots are utilised to study the effect of key parameters, such as gate operation times, and random variables, such as the initial fields required to start the iterative algorithm. Core characteristics of the optimal fields are statistically analysed. Substantial differences between Markovian and non-Markovian environments in terms of the possibilities for control and the control mechanisms are uncovered. In particular, in the Markovian case it is found that the optimal fields obtained without considering the environment cannot be improved substantially by taking the environment into account and the fidelities attained are determined mostly by the gate operation time as well as the overall strength of the environmental effects. Computation time is saved if the fields are pre-optimised neglecting decoherence. In the non-Markovian case, on the other hand, substantial improvements in the fidelities are observed when the details of the system-bath coupling are taken into account. In that case, field leakage is shown to be a significant issue which can make high gate fidelities impossible to obtain unless both the system and noise qubits are fully controlled.

quant-ph↗

arXiv2012

Quantum system characterization with limited resources

The construction and operation of large scale quantum information devices presents a grand challenge. A major issue is the effective control of coherent evolution, which requires accurate knowledge of the system dynamics that may vary from device to device. We review strategies for obtaining such knowledge from minimal initial resources and in an efficient manner, and apply these to the problem of characterization of a qubit embedded into a larger state manifold, made tractable by exploiting prior structural knowledge. We also investigate adaptive sampling for estimation of multiple parameters.

quant-ph↗

arXiv2012

Symmetries on Spin Chains: Limited Controllability and Minimal Controls for Full Controllability

Symmetry is a fundamentally important concept in many branches of physics. In this work, we discuss two types of symmetries, external symmetry and internal symmetry, which appear frequently in controlled quantum spin chains and apply them to study various controllability problems. For spin chains under single local end control when external symmetries exists, we can rigorously prove that the system is controllable in each of the invariant subspaces for both XXZ and XYZ chains, but not for XX or Ising chains. Such results have direct applications in controlling antiferromagnetic Heisenberg chains when the dynamics is naturally confined in the largest excitation subspace. We also address the theoretically important question of minimal control resources to achieve full controllability over the entire spin chain space. In the process we establish a systematic way of evaluating the dynamical Lie algebras and using known symmetries to help identify the dynamical Lie algebra.

quant-ph↗