12,867 research outputs found
Distributed measurement-based quantum computation
We develop a formal model for distributed measurement-based quantum
computations, adopting an agent-based view, such that computations are
described locally where possible. Because the network quantum state is in
general entangled, we need to model it as a global structure, reminiscent of
global memory in classical agent systems. Local quantum computations are
described as measurement patterns. Since measurement-based quantum computation
is inherently distributed, this allows us to extend naturally several concepts
of the measurement calculus, a formal model for such computations. Our goal is
to define an assembly language, i.e. we assume that computations are
well-defined and we do not concern ourselves with verification techniques. The
operational semantics for systems of agents is given by a probabilistic
transition system, and we define operational equivalence in a way that it
corresponds to the notion of bisimilarity. With this in place, we prove that
teleportation is bisimilar to a direct quantum channel, and this also within
the context of larger networks.Comment: 17 page
Entanglement as a semantic resource
The characteristic holistic features of the quantum theoretic formalism and the intriguing notion of entanglement can be applied to a field that is far from microphysics: logical semantics. Quantum computational logics are new forms of quantum logic that have been suggested by the theory of quantum logical gates in quantum computation. In the standard semantics of these logics, sentences denote quantum information quantities: systems of qubits (quregisters) or, more generally, mixtures of quregisters (qumixes), while logical connectives are interpreted as special quantum logical gates (which have a characteristic reversible and dynamic behavior). In this framework, states of knowledge may be entangled, in such a way that our information about the whole determines our information about the parts; and the procedure cannot be, generally, inverted. In spite of its appealing properties, the standard version of the quantum computational semantics is strongly "Hilbert-space dependent". This certainly represents a shortcoming for all applications, where real and complex numbers do not generally play any significant role (as happens, for instance, in the case of natural and of artistic languages). We propose an abstract version of quantum computational semantics, where abstract qumixes, quregisters and registers are identified with some special objects (not necessarily living in a Hilbert space), while gates are reversible functions that transform qumixes into qumixes. In this framework, one can give an abstract definition of the notions of superposition and of entangled pieces of information, quite independently of any numerical values. We investigate three different forms of abstract holistic quantum computational logic
Automated Verification of Quantum Protocols using MCMAS
We present a methodology for the automated verification of quantum protocols
using MCMAS, a symbolic model checker for multi-agent systems The method is
based on the logical framework developed by D'Hondt and Panangaden for
investigating epistemic and temporal properties, built on the model for
Distributed Measurement-based Quantum Computation (DMC), an extension of the
Measurement Calculus to distributed quantum systems. We describe the
translation map from DMC to interpreted systems, the typical formalism for
reasoning about time and knowledge in multi-agent systems. Then, we introduce
dmc2ispl, a compiler into the input language of the MCMAS model checker. We
demonstrate the technique by verifying the Quantum Teleportation Protocol, and
discuss the performance of the tool.Comment: In Proceedings QAPL 2012, arXiv:1207.055
A Formal Model of Metaphor in Frame Semantics
A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a wave function in Hilbert space. The practical way for a probability distribution and a corresponding wave function to be assigned to a given
metaphor in a given language is considered. A series of formal definitions is deduced from this for: “representation”, “reality”, “language”, “ontology”, etc. All are based on Hilbert space. A few statements about a quantum computer are implied: The sodefined reality is inherent and internal to it. It can report a result only “metaphorically”. It will demolish transmitting the result “literally”, i.e. absolutely exactly. A new and different formal
definition of metaphor is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above. The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought. Four areas of cognition are unified as different but isomorphic interpretations of the mathematical model based on Hilbert space. These are: quantum mechanics, frame semantics, formal semantics by
means of quantum computer, and the theory of metaphor in
linguistics
Analysis of Quantum Entanglement in Quantum Programs using Stabilizer Formalism
Quantum entanglement plays an important role in quantum computation and
communication. It is necessary for many protocols and computations, but causes
unexpected disturbance of computational states. Hence, static analysis of
quantum entanglement in quantum programs is necessary. Several papers studied
the problem. They decided qubits were entangled if multiple qubits unitary
gates are applied to them, and some refined this reasoning using information
about the state of each separated qubit. However, they do not care about the
fact that unitary gate undoes entanglement and that measurement may separate
multiple qubits. In this paper, we extend prior work using stabilizer
formalism. It refines reasoning about separability of quantum variables in
quantum programs.Comment: In Proceedings QPL 2015, arXiv:1511.0118
A quantum computational semantics for epistemic logical operators. Part I: epistemic structures
Some critical open problems of epistemic logics can be investigated in the framework
of a quantum computational approach. The basic idea is to interpret sentences like
“Alice knows that Bob does not understand that π is irrational” as pieces of quantum information
(generally represented by density operators of convenient Hilbert spaces). Logical
epistemic operators (to understand, to know. . .) are dealt with as (generally irreversible)
quantum operations, which are, in a sense, similar to measurement-procedures. This approach
permits us to model some characteristic epistemic processes, that concern both human
and artificial intelligence. For instance, the operation of “memorizing and retrieving
information” can be formally represented, in this framework, by using a quantum teleportation
phenomenon
Applying quantitative semantics to higher-order quantum computing
Finding a denotational semantics for higher order quantum computation is a
long-standing problem in the semantics of quantum programming languages. Most
past approaches to this problem fell short in one way or another, either
limiting the language to an unusably small finitary fragment, or giving up
important features of quantum physics such as entanglement. In this paper, we
propose a denotational semantics for a quantum lambda calculus with recursion
and an infinite data type, using constructions from quantitative semantics of
linear logic
High-Level Methods for Quantum Computation and Information
A research programme is set out for developing the use of high-level methods
for quantum computation and information, based on the categorical formulation
of quantum mechanics introduced by the author and Bob Coecke.Comment: 5 page
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