arXiv subjects

Sophie G Schirmer

Publications and source records attributed to Sophie G Schirmer.

4 recordsLinked to original sources

arXiv2017

Design of Feedback Control Laws for Information Transfer in Spintronics Networks

Information encoded in networks of stationary, interacting spin-1/2 particles is central for many applications ranging from quantum spintronics to quantum information processing. Without control, however, information transfer through such networks is generally inefficient. Currently available control methods to maximize the transfer fidelities and speeds mainly rely on dynamic control using time-varying fields and often assume instantaneous readout. We present an alternative approach to achieving efficient, high-fidelity transfer of excitations by shaping the energy landscape via the design of time-invariant feedback control laws without recourse to dynamic control. Both instantaneous readout and the more realistic case of finite readout windows are considered. The technique can also be used to freeze information by designing energy landscapes that achieve Anderson localization. Perfect state or super-optimal transfer and localization are enabled by conditions on the eigenstructure of the system and signature properties for the eigenvectors. Given the eigenstructure enabled by super-optimality, it is shown that feedback controllers that achieve perfect state transfer are, surprisingly, also the most robust with regard to uncertainties in the system and control parameters.

quant-ph↗

arXiv2011

Efficient Algorithms for Optimal Control of Quantum Dynamics: The "Krotov'' Method unencumbered

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.

quant-ph↗

arXiv2011

Symmetry & Controllability for Spin Networks with a Single-Node Control

We consider the relation of symmetries and subspace controllability for spin networks with XXZ coupling subject to control of a single node by a local potential (Z-control). Such networks decompose into excitation subspaces. Focusing on the single excitation subspace it is shown that for single-node Z-controls external symmetries are characterized by eigenstates of the system Hamiltonian that have zero overlap with the control node, and there are no internal symmetries. It is further shown that there are symmetries that persist even in the presence of random perturbations. For uniformly coupled XXZ chains a characterization of all possible symmetries is given, which shows a strong dependence on the position of the node we control. Finally, it is shown rigorously for uniform Heisenberg and XX chains subject to single-node Z-control that the lack of symmetry is not only necessary but sufficient for subspace controllability. The latter approach is then generalized to establish controllability results for simple branched networks.

quant-ph↗

arXiv2010

Robust Entanglement in Anti-ferromagnetic Heisenberg Chains by Single-spin Optimal Control

We demonstrate how near-perfect entanglement (in fact arbitrarily close to maximal entanglement) can be generated between the end spins of an anti-ferromagnetic isotropic Heisenberg chain of length $N$, starting from the ground state in the $N/2$ excitation subspace, by applying a magnetic field along a given direction, acting on a single spin only. Temporally optimal magnetic fields to generate a singlet pair between the two end spins of the chain are calculated for chains up to length 20 using optimal control theory. The optimal fields are shown to remain effective in various non-ideal situations including thermal fluctuations, magnetic field leakage, random system couplings and decoherence. Furthermore, the quality of the entanglement generated can be substantially improved by taking these imperfections into account in the optimization. In particular, the optimal pulse of a given thermal initial state is also optimal for any other initial thermal state with lower temperature.

quant-ph↗