Related papers: Rational Quantum Mechanics: Testing Quantum Theory…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
Quantum mechanics in the Rigged Hilbert Space formulation describes quasistationary phenomena mathematically rigorously in terms of Gamow vectors. We show that these vectors exhibit microphysical irreversibility, related to an intrinsic…
The mathematical notion of incompleteness (eg of rational numbers, Turing-computable functions, and arithmetic proof) does not play a key role in conventional physics. Here, a reformulation of the kinematics of quantum theory is attempted,…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
Quantum computation is a subject of much theoretical promise, but has not been realized in large scale, despite the discovery of fault-tolerant procedures to overcome decoherence. Part of the reason is that the theoretically modest…
Quantum computing exploits fundamentally new models of computation based on quantum mechanical properties instead of classical physics, and it is believed that quantum computers are able to dramatically improve computational power for…
Kempf et al. in Ref. [1] have formulated a Hilbert space representation of quantum mechanics with a minimal measurable length. Recently it has been revealed, in the context of doubly special relativity, that a test particles' momentum…
Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. Owing to the intimate…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
We derive the Hilbert space formalism of quantum mechanics from epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. An…
As neural networks are known to efficiently represent classes of tensor-network states as well as volume-law-entangled states, identifying which properties determine the representational capabilities of neural quantum states (NQS) remains…
The aim of this paper is to enlight the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the…
Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
The formalism of quantum theory in Hilbert space has been applied with success to the modeling and explanation of several cognitive phenomena, whereas traditional cognitive approaches were problematical. However, this 'quantum cognition…
We investigate the fundamental expressivity limits of quantum reservoir computing (QRC) by establishing a formal connection to parametrized quantum circuit quantum machine learning (PQC-QML). We analytically prove, and numerically…
One of the fundamental theories of physics is that of quantum mechanics. Quantum mechanics tries to explain the inconsistencies in the behaviors of systems at the macro and micro scales. Quantum mechanics paved the way for quantum computing…
The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is,…