49,353 research outputs found
Swap logic
We investigate dynamic modal operators that can change the model during evaluation. We define the logic SL by extending the basic modal language with the ♦ modality, which is a diamond operator that in addition has the ability to invert pairs of related elements in the domain while traversing an edge of the accessibility relation. SL is very expressive: it fails to have the finite and the tree model property. We show that SL is equivalent to a fragment of first-order logic by providing a satisfiability preserving translation. In addition, we provide an equivalence preserving translation from SL to the hybrid logic H(:, ↓). We also define a suitable notion of bisimulation for SL and investigate its expressive power, showing that it lies strictly between the basic modal logic and H(:, ↓). We finally show that its model checking problem is PSpace-complete and its satisfiability problem is undecidable.http://dx.doi.org/10.1093/jigpal/jzt030submittedVersionFil: Areces, Carlos Eduardo. Universidad Nacional de CĂłrdoba. Facultad de Matemática, AstronomĂa y FĂsica; Argentina.Fil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina.Fil: Fervari, RaĂşl Alberto. Universidad Nacional de CĂłrdoba. Facultad de Matemática, AstronomĂa y FĂsica; Argentina.Fil: Hoffmann, Guillaume Emmanuel. Universidad Nacional de CĂłrdoba. Facultad de Matemática, AstronomĂa y FĂsica; Argentina.Ciencias de la ComputaciĂł
Spin swap gate in the presence of qubit inhomogeneity in a double quantum dot
We study theoretically the effects of qubit inhomogeneity on the quantum
logic gate of qubit swap, which is an integral part of the operations of a
quantum computer. Our focus here is to construct a robust pulse sequence for
swap operation in the simultaneous presence of Zeeman inhomogeneity for quantum
dot trapped electron spins and the finite-time ramp-up of exchange coupling in
a double dot. We first present a geometric explanation of spin swap operation,
mapping the two-qubit operation onto a single-qubit rotation. We then show that
in this geometric picture a square-pulse-sequence can be easily designed to
perform swap in the presence of Zeeman inhomogeneity. Finally, we investigate
how finite ramp-up times for the exchange coupling negatively affect the
performance of the swap gate sequence, and show how to correct the problems
numerically.Comment: published versio
Non-deterministic algebraization of logics by swap structures1
Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics
Relation-Changing Logics as Fragments of Hybrid Logics
Relation-changing modal logics are extensions of the basic modal logic that
allow changes to the accessibility relation of a model during the evaluation of
a formula. In particular, they are equipped with dynamic modalities that are
able to delete, add, and swap edges in the model, both locally and globally. We
provide translations from these logics to hybrid logic along with an
implementation. In general, these logics are undecidable, but we use our
translations to identify decidable fragments. We also compare the expressive
power of relation-changing modal logics with hybrid logics.Comment: In Proceedings GandALF 2016, arXiv:1609.0364
Controlled exchange interaction for quantum logic operations with spin qubits in coupled quantum dots
A two-electron system confined in two coupled semiconductor quantum dots is
investigated as a candidate for performing quantum logic operations on spin
qubits. We study different processes of swapping the electron spins by
controlled switching on/off the exchange interaction. The resulting spin swap
corresponds to an elementary operation in quantum information processing. We
perform a direct time evolution simulations of the time-dependent Schroedinger
equation. Our results show that -- in order to obtain the full interchange of
spins -- the exchange interaction should change smoothly in time. The presence
of jumps and spikes in the corresponding time characteristics leads to a
considerable increase of the spin swap time. We propose several mechanisms to
modify the exchange interaction by changing the confinement potential profile
and discuss their advantages and disadvantages
Swap structures semantics for Ivlev-like modal logics
In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally a non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras
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