Related papers: (Un)decidable Problems about Reachability of Quant…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over discrete time. We analyse this problem with respect to the allowable control sets, which in general are assumed to be defined by…
The paper deals with the verification of reachability properties in a commonly used state transition model of communication protocols, which consists of finite state machines connected by potentially unbounded FIFO channels. Although simple…
This paper deals with the problem of point-to-point reachability in multi-linear systems. These systems consist of a partition of the Euclidean space into a finite number of regions and a constant derivative assigned to each region in the…
The undecidability of basic decision problems for general FIFO machines such as reachability and unboundedness is well-known. In this paper, we provide an underapproximation for the general model by considering only runs that are…
Significant advances in the development of computing devices based on quantum effects and the demonstration of their use to solve various problems have rekindled interest in the nature of the "quantum computational advantage." Although…
The problem of computing the reachable set for a given system is a quintessential question in nonlinear control theory. While previous work has yielded a plethora of approximate and analytical methods for determining such a set, these…
A physical system is determined by a finite set of initial conditions and "laws" represented by equations. The system is computable if we can solve the equations in all instances using a "finite body of mathematical knowledge". In this…
A control system consists of a plant component and a controller which periodically computes a control input for the plant. We consider systems where the controller is implemented by a feedforward neural network with ReLU activations. The…
The study of Markov models is central to control theory and machine learning. A quantum analogue of partially observable Markov decision process was studied in (Barry, Barry, and Aaronson, Phys. Rev. A, 90, 2014). It was proved that…
In this work, we show that very natural, apparently simple problems in quantum measurement theory can be undecidable even if their classical analogues are decidable. Undecidability hence appears as a genuine quantum property here. Formally,…
This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of…
The reachable set for a finite dimensional quantum system is shown to be the orbit of the group corresponding to the internal and control Hamiltonians, even if this group is not compact.
Recent work has examined how undecidable problems can arise in quantum information science. We augment this by introducing three new undecidable problems stated in terms of tensor networks. These relate to ideas of Penrose about the…
In recent years, Arenz et al. proposed the idea of reachable set characterization based on the quantum speed limit (QSL); that is, the reachable set of the target unitary gate in a closed qubit system can be characterized by considering the…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…
In this paper, the physical realizability property is investigated for a class of nonlinear quantum systems. This property determines whether a given set of nonlinear quantum stochastic differential equations corresponds to a physical…
Determining the reachable set for a given nonlinear system is critically important for autonomous trajectory planning for reach-avoid applications and safety critical scenarios. Providing the reachable set is generally impossible when the…
We consider reachability decision problems for linear dynamical systems: Given a linear map on $\mathbb{R}^d$ , together with source and target sets, determine whether there is a point in the source set whose orbit, obtained by repeatedly…