Related papers: Logical aspects of quantum structures
We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way,…
We examine a few problems of enumerative geometry and present their solutions in the framework of deformed (quantum) cohomology rings.
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
In this paper we give an overview of the quantum computational complexity class QMA and a description of known QMA-complete problems to date. Such problems are believed to be difficult to solve, even with a quantum computer, but have the…
The main contribution of this paper is the introduction of a dynamic logic formalism for reasoning about information flow in composite quantum systems. This builds on our previous work on a complete quantum dynamic logic for single systems.…
The existence of small amounts of advanced radiation, or a tilt in the arrow of time, makes the basic equations of physics mixed-type functional differential equations. The novel features of such equations point to a microphysical structure…
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…
Logical gates studied in quantum computation suggest a natural logical abstraction that gives rise to a new form of unsharp quantum logic. We study the logical connectives corresponding to the following gates: the Toffoli gate, the NOT and…
This is an attempt to illustrate the glorious history of logical foundations and to discuss the uncertain future.
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain which can be compared wrt. equality. As the satisfiability problem for this logic is undecidable in general, in…
In a series of papers in the last ten years, various aspects of the mathematical foundations of the quantum theory of atoms in molecules have been considered by this author and his coworkers in some details. Although these considerations…
A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of…
A rough overview is given over the most essential structures underlying all working quantum theoretical models as well as axiomatic and algebraic quantum field theory .
Quantum logic (QL) is a non-classical logic for analyzing the propositions of quantum physics. Modal logic MB, which is a logic that handles the value of the inner product that appears in quantum mechanics, was constructed with the…
This paper deals with the foundations of quantum mechanics. We start by outlining the characterisation, due to Birkhoff and Von Neumann, of the logical structures of the theories of classical physics and quantum mechanics, as boolean and…
We search for a possible mathematical formulation of some of the key ideas of the relational interpretation of quantum mechanics and study their consequences. We also briefly overview some proposals of relational quantum mechanics for an…
In this paper, we study quatization condition of logsymplectic struc- ture using integrality of such structue on the complement of associated divisor D.
Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
Many theoretical predictions derived from quantum mechanics have been confirmed experimentally during the last 80 years. However, interpretative aspects have long been subject to debate. Among them, the question of the existence of hidden…