SIAM Journal on Computing
Quantum computation and quantum information
Quantum computation and quantum information
A Foundation of Programming a Multi-tape Quantum Turing Machine
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
Halting of Quantum Turing Machines
UMC '02 Proceedings of the Third International Conference on Unconventional Models of Computation
Classically controlled quantum computation
Mathematical Structures in Computer Science
Universality and programmability of quantum computers
Theoretical Computer Science
Logical reversibility of computation
IBM Journal of Research and Development
Strongly Universal Quantum Turing Machines and Invariance of Kolmogorov Complexity
IEEE Transactions on Information Theory
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The quantum Turing machine (QTM) has been introduced by Deutsch as an abstract model of quantum computation. The transition function of a QTM is linear, and has to be unitary to be a well-formed QTM. This well-formedness condition ensures that the evolution of the machine does not violate the postulates of quantum mechanics. However, we claim in this paper that the well-formedness condition is too strong and we introduce a weaker condition, leading to a larger class of Turing machines called Observable Quantum Turing Machines (OQTMs). We prove that the evolution of such OQTM does not violate the postulates of quantum mechanics while offering a more general abstract model for quantum computing. This novel abstract model unifies classical and quantum computations, since every well-formed QTM and every deterministic TM are OQTMs, whereas a deterministic TM has to be reversible to be a well-formed QTM. In this paper we introduce the fundamentals of OQTM like a well-observed lemma and a completion lemma. The introduction of such an abstract machine allowing classical and quantum computations is motivated by the emergence of models of quantum computation like the one-way model. More generally, the OQTM aims to be an abstract framework for the pragmatic paradigm of quantum computing: quantum data, classical control'. Furthermore, this model allows a formal and rigorous treatment of problems requiring classical interactions, like the halting of QTM. Finally, it opens new perspectives for the construction of a universal QTM.