相关论文: A Generalized Quantifier Concept in Computational …
We establish a direct connection between spread complexity and quantum circuit complexity by demonstrating that spread complexity emerges as a limiting case of a circuit complexity framework built from two fundamental operations:…
Variational quantum algorithms that are used for quantum machine learning rely on the ability to automatically differentiate parametrized quantum circuits with respect to underlying parameters. Here, we propose the rules for differentiating…
A generic computation of a subset $A$ of $\mathbb{N}$ is a computation which correctly computes most of the bits of $A$, but which potentially does not halt on all inputs. The motivation for this concept is derived from complexity theory,…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
In this paper we construct the quantum Virasoro algebra ${\mathcal{L}}_{c}$ generators in terms of operators of the generalized Clifford algebras $C_{n}^{k}$. Precisely, we show that ${\mathcal{L}}_{c}$ can be embedded into generalized…
Generalizations of the q-Onsager algebra are introduced and studied. In one of the simplest case and q=1, the algebra reduces to the one proposed by Uglov-Ivanov. In the general case and $q\neq 1$, an explicit algebra homomorphism…
A generalization of the concept of twisted internal coHom object in the category of conic quantum spaces (c.f. math.QA/0112233) was outlined in math.QA/0202205. The aim of this article is to discuss in more detail this generalization.
The use of the quantizer-dequantizer formalism to describe the evolution of a quantum system is reconsidered. We show that it is possible to embed a manifold in the space of quantum states of a given auxiliary system by means of an…
We study the Universality and Membership Problems for gate sets consisting of a finite number of quantum gates. Our approach relies on the techniques from compact Lie groups theory. We also introduce an auxiliary problem called Subgroup…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
The logarithmic representation of infinitesimal generators is generalized to the cases when the evolution operator is unbounded. The generalized result is applicable to the representation of infinitesimal generators of unbounded evolution…
Abstraction is key to human and artificial intelligence as it allows one to see common structure in otherwise distinct objects or situations and as such it is a key element for generality in AI. Anti-unification (or generalization) is…
A scheme of universal quantum computation on a chain of qubits is described that does not require local control. All the required operations, an Ising-type interaction and spatially uniform simultaneous one-qubit gates, are…
Studies of geometrical theories suggest that fundmental problems of quantization arise from the disparate usage of displacement operators. These may be the source of a concealed inconsistency in the accepted formalism of quantum physics.…
Many insights into the quantum world can be found by studying it from amongst more general operational theories of physics. In this thesis, we develop an approach to the study of such theories purely in terms of the behaviour of their…
The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas--e.g., deductive databases, theorem proving, static…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
In recent papers and books, a global quantization has been developed for unimodular groups of type I. It involves operator-valued symbols defined on the product between the group $\mathsf{G}$ and its unitary dual $\widehat{\mathsf{G}}$,…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…