The cluster state represents a highly entangled state which is one central object for measurementbased quantum computing. Here we study the robustness of the cluster state on the two-dimensional square lattice at zero temperature in the presence of external magnetic fields by means of different types of high-order series expansions and variational techniques using infinite Projected Entangled Pair States (iPEPS). The phase diagram displays a first-order phase transition line ending in two critical end points. Furthermore, it contains a characteristic self-dual line in parameter space allowing many precise statements. The self-duality is shown to exist on any lattice topology. I. MOTIVATIONThe exploitation of quantum mechanics to build a quantum computer is a very active area in current research, because it is expected to be capable of solving classically hard problems in a polynomial amount of time 1 yielding a deeper understanding of the quantum world. To this end it has been shown that a universal quantum computer can be built by only a small set of elementary operations, namely arbitrary single-qubit rotations plus certain two-qubit gates like CZ or cNOT 2,3 . Especially the two-qubit operations turn out to be complicated to implement in experiment.Measurement-based quantum computing is a fascinating alternative approach for a quantum computer 4 . The essential idea is to prepare a highly-entangled initial quantum state on which only single-qubit measurement are sufficient to run a quantum algorithm. Meaurements with respect to an arbitrary basis are easy to perform in experiment. This feature comes with the price, that the initial state is hard to prepare in nature. One class of such highly-entangled states useful for measurementbased quantum computation are cluster states.One natural way of realizing a cluster state would be to cool down appropriate Hamiltonians having the cluster state as a ground state. Indeed, so-called cluster Hamiltonians exist but contain typically multi-site interactions which are very rare in nature. As a consequence, simpler models containing solely two-spin interactions have been proposed in the literature having the cluster Hamiltonian as an effective low-energy model. But it has been shown recently that it is very challenging to protect approximative cluster states against additional perturbations 5 . Another approach to study such systems efficiently, could be to prepare the cluster Hamiltonian with a quantum simulator 6-8 . However simulating multi-spin interactions with respect to the desired topology will probably be a challenge.In any case it is important to check whether the cluster state is stable and protected against additional perturbations. This has been the subject of several works in recent years which mostly concentrate on additional magnetic fields as a perturbation 9,10 . The latter studies either investigated the change of entanglement of the perturbed cluster state or explored the complete breakdown of the cluster state due to a phase transition which serves a...

The aim of this work is to study the physical properties of a one-way quantum computer in an effective low-energy cluster state. We calculate the optimal working conditions as a function of the temperature and of the system parameters. The central result of our work is that any effective cluster state implemented in a perturbative framework is fragile against special kinds of external perturbations. Qualitative aspects of our work are important for any implementation of effective low-energy models containing strong multisite interactions.

Background: With the recent advent of inductive charging systems all major automotive manufacturers develop concepts to wirelessly charge electric vehicles. Efficient designs require virtual prototyping that accounts for electromagnetic and thermal fields. The coupled simulations can be computationally very costly. This is because of the high frequencies in the electromagnetic part. This paper derives a mixed frequency-transient model as approximation to the original problem. We propose a co-simulation such that the electromagnetic part is simulated in the frequency domain while the thermal part remains in time domain. Results: The iteration scheme for the frequency-transient model is convergent for high frequency excitation. The error bound improves quadratically with increasing frequency. Conclusions:The frequency-transient model is very efficient for coupled heat-electromagnetic simulations since the time scales typically differ by several orders of magnitude. The time steps of the full system can be chosen according to the heat subsystem only. MSC: 35K05; 35Q61; 65Z05; 78A25; 78M12; 80M25

This article presents a novel approach for motion pattern generation for humanoid robots combining the intuitive specification via key frames and the robustness of a ZMP stability controller. Especially the execution of motions interacting with the robot's environment tends to result in very different stability behavior depending on the exact moment, position and force of interaction, thus providing problems for the classical replay of prerecorded motions. The proposed method is applied to several test cases including the design of kicking motions for humanoid soccer robots and evaluated in real world experiments which clearly show the benefit of the approach.

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