Abstract
Unlike the standard Quantum Computational Logic (QCL), where the carrier of information (target) is conventionally assumed to be only the last qubit over a sequence of many qubits, here we propose an extended version of the QCL (we call Multi Target Quantum Computational Logic) where the number and the position of the target qubits are arbitrary.
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Notes
It is easy to see that \(Swap_{[k;m,m+n-1]}^{-1}=Swap_{[k;m,m+n-1]}\) for any value of k, m and n.
Let us give a slight abuse of the terms target and control remarking that, for example, if we refer to the picture of the Sect. 3, the qubit \(\vert {x_1} \rangle\) is not a control qubit but, accordingly with this notation, it assumes a control position over the quantum circuit where it is located.
Notice that the probability \({\texttt {p}}\) we refer to is the one introduced in the context of the standard QCL (see Eq. 4.1). On this basis, we are using this example to express the MT-QCL probability \({\texttt {P}}\) in terms of the QCL probability \({\texttt {p}}\).
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Acknowledgements
This work is partially supported by Regione Autonoma della Sardegna within the project “Time-logical evolution of correlated microscopic systems” CRP 55, L.R. 7/2007 (2015) and by Fondazione Sardegna within the project “Strategies and Technologies for Scientific Education and Dissemination” (2017).
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Sergioli, G. Towards a Multi Target Quantum Computational Logic. Found Sci 25, 87–104 (2020). https://doi.org/10.1007/s10699-018-9569-8
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DOI: https://doi.org/10.1007/s10699-018-9569-8