Related papers: (Un)decidable Problems about Reachability of Quant…
We present and study new definitions of universal and programmable universal unary functions and consider a new simplicity criterion: almost decidability of the halting set. A set of positive integers S is almost decidable if there exists a…
Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology and cryptography. Yet, there is no universally efficient method for quantifying coherence either in…
We propose a solution to a time-varying variant of Markov Decision Processes which can be used to address decision-theoretic planning problems for autonomous systems operating in unstructured outdoor environments. We explore the time…
We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively…
This paper considers the realizability of quantum gates from the perspective of information complexity. Since the gate is a physical device that must be controlled classically, it is subject to random error. We define the complexity of gate…
The quantum coherence of a multipartite system is investigated when some of the parties are moving with uniform acceleration and the analysis is carried out using the single mode approximation. Due to acceleration the quantum coherence is…
The question of open-loop control in the Gaussian regime may be cast by asking which Gaussian unitary transformations are reachable by turning on and off a given set of quadratic Hamiltonians. For compact groups, including finite…
Reachability for piecewise affine systems is known to be undecidable, starting from dimension $2$. In this paper we investigate the exact complexity of several decidable variants of reachability and control questions for piecewise affine…
In simple -- but selected -- quantum systems, the probability distribution determined by the ground state wave function is infinitely divisible. Like all simple quantum systems, the Euclidean temporal extension leads to a system that…
Quantum computers are hypothetical devices, based on quantum physics, that would enable us to perform certain computations hundreds of orders of magnitude faster than digital computers. This feature is coined as "quantum supremacy" and one…
There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a…
We consider the separability of various joint states of D-dimensional quantum systems, which we call "qudits." We derive two main results: (i) the separability condition for a two-qudit state that is a mixture of the maximally mixed state…
We point out that some questions in quantum field theory are undecidable in a precise mathematical sense. More concretely, it will be demonstrated that there is no algorithm answering whether a given 2d supersymmetric Lagrangian theory…
A complete characterization of the complexity of the reachability problem for vector addition system has been open for a long time. The problem is shown to be Tower complete.
This article focuses on the connection between the possibility of quantum computers, the predictability of complex quantum systems in nature, and the issue of free will.
Using new results on the separability properties of bosonic systems, we provide a new complete criterion for separability. This criterion aims at characterizing the set of separable states from the inside by means of a sequence of…
The spectral gap problem - determining whether the energy spectrum of a system has an energy gap above ground state, or if there is a continuous range of low-energy excitations - pervades quantum many-body physics. Recently, this important…
We study pushdown vector addition systems, which are synchronized products of pushdown automata with vector addition systems. The question of the boundedness of the reachability set for this model can be refined into two decision problems…
We find exact solutions for a universal set of quantum gates on a scalable candidate for quantum computers, namely an array of two level systems. The gates are constructed by a combination of dynamical and geometrical (non-Abelian) phases.…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…