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The quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for $N$-dimensional quantum systems is presented. This generalized concurrence has potential…
This paper introduces a special type of systems, defines their properties, and then demonstrates that a reduction machine for pure untyped extensional lambda calculus can be implemented as a system of the introduced type. Specifically, we…
For quantum Turing machines we present three elements: Its components, its time evolution operator and its local transition function. The components are related with the components of deterministic Turing machines, the time evolution…
In this work we consider a dynamic system consisting of a damped harmonic oscillator and we formalize a Turing Machine whose definition in terms of states, alphabet and transition rules, can be considered equivalent to that of the…
We introduce $\mathsf{LEM}$, a type-assignment system for the linear $ \lambda $-calculus that extends second-order $\mathsf{IMLL}_2$, i.e., intuitionistic multiplicative Linear Logic, by means of logical rules that weaken and contract…
An earlier paper gave a means of calculating the Lamb shift via Feynman diagrams. Here we apply the same techniques to TQFT.
The lambda calculus since more than half a century is a model and foundation of functional programming languages. However, lambda expressions can be evaluated with different reduction strategies and thus, there is no fixed cost model nor…
We consider the call-by-value lambda-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent…
Quantum machine learning deals with leveraging quantum theory with classic machine learning algorithms. Current research efforts study the advantages of using quantum mechanics or quantum information theory to accelerate learning time or…
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such…
This paper introduces a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification…
We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…
Transformers are being used extensively across several sequence modeling tasks. Significant research effort has been devoted to experimentally probe the inner workings of Transformers. However, our conceptual and theoretical understanding…
Quantum interference is proposed as a tool to augment Quantum Computation.
Geometrical Computation as a new model of computation is the counterpart of Cellular Automata that has Turing computing ability. In this paper we provide an algorithm to simulate Alternating Turing Machine in the context of Signal Machine…
We will extend the well-known Church encoding of Boolean logic into $\lambda$-calculus to an encoding of McCarthy's $3$-valued logic into a suitable infinitary extension of $\lambda$-calculus that identifies all unsolvables by $\bot$, where…
Kuroda's translation embeds classical first-order logic into intuitionistic logic, through the insertion of double negations. Recently, Brown and Rizkallah extended this translation to higher-order logic. In this paper, we adapt it for…
The development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation, and sensing. This poses severe challenges in efficient control,…
This paper discusses how to implement certain classes of quantum computer algorithms using classical discrete switching networks that are amenable to implementation in main stream CMOS transistor IC technology. The methods differ from other…
In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard…