Related papers: Quantum polymorphism characterisation of commutati…
Here we demonstrate, firstly, the construction of dualities using the exact renormalization group approach and, secondly, that spatial non-commutativity can emerge as such a duality. This is done in a simple quantum mechanical setting that…
Group equivariant neural networks have proven effective in modelling a wide range of tasks where the data lives in a classical geometric space and exhibits well-defined group symmetries. However, these networks are not suitable for learning…
We present an infinite sequence of finite graphs with trivial automorphism group and non-trivial quantum automorphism group. These are the first known examples of graphs with this property. Moreover, to the best of our knowledge, these are…
Recently, a standardized framework was proposed for introducing quantum-inspired moves in mathematical games with perfect information and no chance. The beauty of quantum games-succinct in representation, rich in structures, explosive in…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
Incompatibility of quantum devices is one of the cornerstones of quantum theory, and the incompatibility of quantum measurements and channels has been linked to quantum advantage in certain information theoretic tasks. In this work, we…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
Motivated by the vast literature of quantum automorphism groups of graphs, we define and study quantum automorphism groups of matroids. A key feature of quantum groups is that there are many quantizations of a classical group, and this…
Based on the connection between the categorical derivation of classical programs from specifications and the category-theoretic approach to quantum physics, this paper contributes to extending the laws of classical program algebra to…
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
The intention of this thesis is to provide general tools and concepts that allow to perform a mathematically substantiated symmetry reduction in (quantum) gauge field theories. Here, the main focus is on the framework of loop quantum…
We propose categories of $1$-dimensional and multi-dimensional quantum walks. In the categories, an object is a quantum walk, and a morphism is an intertwining operator between two quantum walks. The new framework enables us to discuss…
The Symmetric group $S_{n}$ manifests itself in large classes of quantum systems as the invariance of certain characteristics of a quantum state with respect to permuting the qubits. The subgroups of $S_{n}$ arise, among many other…
Quantum Mechanics is revisited as the appropriate theoretical framework for the description of the outcome of experiments that rely on the use of classical devices. In particular, it is emphasized that the limitations on the measurability…
Continuous-time quantum hardware implementations generally lack the native capability to implement high-order terms that would facilitate efficient compilation of quantum algorithms. This limitation has, in part, motivated the development…
Perturbative gadgets are used to construct a quantum Hamiltonian whose low-energy subspace approximates a given quantum $k$-body Hamiltonian up to an absolute error $\epsilon$. Typically, gadget constructions involve terms with large…
There is a long-standing debate about whether gravity should be quantised. A powerful line of argument in favour of quantum gravity considers models of hybrid systems consisting of coupled quantum-classical sectors. The conclusion is that…
Let $\mathbb{H}\trianglelefteq\mathbb{G}$ be a closed normal subgroup of a locally compact quantum group. We introduce a strictly positive group-like element affiliated with $L^{\infty}(\mathbb{G})$ that, roughly, measures the failure of…