Quantum Computing and the Principles of Logic

HECTOR C. SABELLI, Gerald H. Thomas

Quantum computing forces a reexamination of logic. We examine its historical roots in logos, the logic of nature, and it is manifested by the laws of physics. A new logic comes out of this inquiry and it is applied to quantum computing. The logical design of computers according to the logic of quantum physics will allow the full use of quantum processes for computation and also adapt our humanly conceived computer logic to the actual logic of nature. The basic principles of quantum physics are homologically repeated in fundamental processes at all levels of organization. Thus, the principles of action, opposition such as charge and spin, chromatic structure, and the creation of novelty, diversity, and complexity can guide logic. Explicit realizations of these ideas are provided.Request access from your librarian to read this chapter's full text.

María Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini +1 more

Hafiz Md. Hasan Babu

Jincheng Zhang

Probability Logic Quantum Computing (PLQC) presents a novel approach to quantum computing by integrating the fundamental principles of probability logic into the core computational process. This research explores the potential of leveraging the inherent strengths of probability logic – such as its ability to handle uncertainty and probabilistic outcomes – to enhance the efficiency and stability of quantum algorithms. The core mechanism focuses on modifying quantum gate operations and quantum circuit design to actively incorporate probabilistic elements, thereby mitigating the inherent challenges of quantum systems. This paper investigates the feasibility of implementing PLQC, outlining its potential benefits and challenges, and providing a preliminary analysis of its design principles. The goal is to establish a robust and scalable framework for quantum computing that surpasses the limitations of traditional approaches.

Michael E. Cuffaro

Vladimir L. Vasyukov

One of the logical proposals that arise from quantum computation is the idea to use the quantum theoretical formalism to represent parallel reasoning. To this aim a quantum computation is considered by means of convenient unitary operators assuming arguments and values in particular sets of qubit systems. Isolating some important unitary operators that have a special role in quantum computation (logical gates or quregisters) we obtain an opportunity to yield the language of Quantum Computational Logic (QCL) (cf. [Cattaneo et al., 2003; Cattaneo et al., 2004; Dalla Chiara et al., 2004]). The basic concept of the semantics of this language is the notion of quantum computational realization such that the meaning associated to any sentence is a quregister. Unlike the semantic of a standard quantum logic QCL-conjunction and QCL-disjunction do not correspond to lattice operations since they are not generally idempotent. Moreover, in QCL the weak distributivity principle breaks down and both the excluded middle and the non contradiction principles are violated. Finally, the axiomatizability of QCL is still an open problem. In the paper an axiomatization of QCL is proposed construing it as a kind of so-called Goldblatt’s binary logic. Some metalogical theorems (paraconsistency and completeness) are proved.