JUCS - Journal of Universal Computer Science 32(3): 357-372, doi: 10.3897/jucs.156960
State transition diagrams for a universal quantum gate set
Anuradha Mahasinghe‡, Ayodhya Liyanage‡‡ University of Colombo, Colombo, Sri Lanka
Corresponding author: Anuradha Mahasinghe ( anuradhamahasinghe@maths.cmb.ac.lk ) © Anuradha Mahasinghe, Ayodhya Liyanage. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Citation:
Mahasinghe A, Liyanage A (2026) State transition diagrams for a universal quantum gate set. JUCS - Journal of Universal Computer Science 32(3): 357-372. https://doi.org/10.3897/jucs.156960 |  |
Abstract
A quantum Turing machine (QTM) is an abstract model of computing that serves as the quantum counterpart of a classical Turing machine. Closely related to the probabilistic Turing machine, a QTM utilises quantum effects such as superposition, entanglement and unitary evolution. Despite its historical role as a framework for devising quantum algorithms and the significance of its classical counterpart in theoretical computing, very little attention has been paid in literature to the state transition of QTM’s for basic quantum gates. In this paper, we construct the state transition diagrams for a set of elementary quantum gates that consists of the Hadamard, CNOT, and T gates, providing a universal basis for fault tolerant quantum computation. We verify the necessary conditions to ensure that the designed state transition diagrams comply with the postulates of quantum mechanics, verifying their well formedness.
Keywords
Quantum computing, Models of computation, Turing machines, Quantum gates, Quantum algorithms