相关论文: Qubit semantics and quantum trees
Quantum Lie algebras $\qlie{g}$ are non-associative algebras which are embedded into the quantized enveloping algebras $U_q(g)$ of Drinfeld and Jimbo in the same way as ordinary Lie algebras are embedded into their enveloping algebras. The…
We propose a quantum programming paradigm where all data are familiar classical data, and the only non-classical element is a random number generator that can return results with negative probability. Currently, the vast majority of quantum…
The emergence of Quantum Machine Learning (QML) to enhance traditional classical learning methods has seen various limitations to its realisation. There is therefore an imperative to develop quantum models with unique model hypotheses to…
In this thesis we use the language of sheaf theory in order to develop a deeper understanding of some of the fundamental differences - such as entanglement, contextuality and non-locality - between quantum and classical physics. We first…
Quantum Field Theory (QFT) represents a vast generalization of Quantum Mechanics (QM), as it deals with systems that have an infinite number of degrees of freedom. The Stone-von Neumann theorem, which establishes the equivalence of…
Quantum signal processing (QSP) is a highly successful algorithmic primitive in quantum computing which leads to conceptually simple and efficient quantum algorithms using the block-encoding framework of quantum linear algebra. Multivariate…
Quantum coherence quantifies the amount of superposition in a quantum system, and is the reason and resource behind several phenomena and technologies. It depends on the natural basis in which the quantum state of the system is expressed,…
Despite its name, Quantum Field Theory (QFT) has been built to describe interactions between localizable particles. For this reason the actual formalism of QFT is partly based on a suitable generalization of the one already used for systems…
We suggest Clifford algebra as a useful simplifying language for present quantum dynamics. Clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups. Aggregates using…
Large language models have demonstrated impressive performance across many domains of mathematics and physics. One natural question is whether such models can support research in highly abstract theoretical fields such as quantum field…
We introduce an algebra qCCS of pure quantum processes in which no classical data is involved, communications by moving quantum states physically are allowed, and computations is modeled by super-operators. An operational semantics of qCCS…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
Entanglement is a non local property of quantum states which has no classical counterpart and plays a decisive role in quantum information theory. Several protocols, like the teleportation, are based on quantum entangled states. Moreover,…
The concept of quantum representation of finite groups (QRFG) has been a fundamental aspect of quantum computing for quite some time, playing a role in every corner, from elementary quantum logic gates to the famous Shor's and Grover's…
Quantum logic aims to capture essential quantum mechanical structure in order-theoretic terms. The Achilles' heel of quantum logic is the absence of a canonical description of composite systems, given descriptions of their components. We…
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schroedinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested…
We show the Standard Model and SuperString Theories can be naturally based on a Quantum Computer foundation. The Standard Model of elementary particles can be viewed as defining a Quantum Computer Grammar and language. A Quantum Computer in…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…