Towards Observable Quantum Turing Machines: Fundamentals, Computational Power, and Universality

Simon Perdrix 1
1 LIG Laboratoire d'Informatique de Grenoble - CAPP
LIG - Laboratoire d'Informatique de Grenoble
Abstract : We study the observation of quantum Turing machines by allowing interactions between a quantum machine and its environment during the computation, whereas a quantum Turing machine --original model introduced by Deutsch-- remains isolated. We show that the introduction of observations leads to a weakening of the well formedness conditions of quantum Turing machines such that any (reversible or not) classical Turing machine is a special instance of a quantum machine. Moreover, observation of quantum Turing machines provides a formal solution to the halting process problem: the impossibility to know whether a given quantum Turing machine has actually reached its halting state. It also provides a more realistic abstract architecture of a quantum computer while most of the physical proposals of quantum computers are based on an hybrid classical-quantum architecture. However, we show that a natural formalisation of an observable quantum Turing machines leads to an over-powerful model solving undecidable problems. As a consequence, we introduce a restricted version of observable quantum Turing machines and we show that, under this restriction, any observable quantum Turing machine can be efficiently simulated by a quantum Turing machine. Finally, we discuss the potential application of the observable quantum Turing machine in the quest of a universal quantum Turing machine while recent papers have pointed out that a classical control is a key feature of a universal quantum machine.
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Submitted on : Wednesday, January 15, 2014 - 12:27:43 PM
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Simon Perdrix. Towards Observable Quantum Turing Machines: Fundamentals, Computational Power, and Universality. International Journal of Unconventional Computing, Old City Publishing, 2011, 7 (4), pp.291-311. ⟨hal-00931402⟩

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