PPubMed16 Jan 2019Cited 6×

Logical Structures Underlying Quantum Computing

Federico Holik, Giuseppe Sergioli, Hector Freytes, Angel Plastino

Abstract

In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.

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The paper proposes a generalized algebraic framework for quantum computational logics that unifies classical and quantum computing and can accommodate various quantum algorithms.

What’s new

i.Generalization of quantum computational logics to handle key quantum algorithms.
ii.Algebraic axiomatization of the generalized logical structures.
iii.Framework for comparing quantum computing with alternative non‑classical theories and guiding algorithm design beyond standard quantum mechanics.

How they did it

The authors review classical deterministic and probabilistic computing, then introduce a generalized quantum computational logic with new notions of equivalence and probabilistic truth values. They formalize these ideas in an axiomatic algebraic framework and illustrate the approach with examples such as the Deutsch‑Jozsa and period‑finding algorithms.

Caveats

✕The work is purely theoretical and lacks experimental validation.
✕Practical implementation details for physical quantum systems are not addressed.
✕Extending the framework to infinite‑dimensional systems and non‑standard quantum theories remains an open challenge.

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