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Coalgebraic Walks, in Quantum and Turing Computation
, 2010
"... Abstract. The paper investigates nondeterministic, probabilistic and quantum walks, from the perspective of coalgebras and monads. Nondeterministic and probabilistic walks are coalgebras of a monad (powerset and distribution), in an obvious manner. It is shown that also quantum walks are coalgebras ..."
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Cited by 7 (5 self)
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Abstract. The paper investigates nondeterministic, probabilistic and quantum walks, from the perspective of coalgebras and monads. Nondeterministic and probabilistic walks are coalgebras of a monad (powerset and distribution), in an obvious manner. It is shown that also quantum walks are coalgebras of a new monad, involving additional control structure. This new monad is also used to describe Turing machines coalgebraically, namely as controlled ‘walks ’ on a tape. 1
1Quantum Iterative Deepening with an application to the Halting problem
"... Classical models of computation traditionally resort to halting schemes in order to enquire about the state of a computation. In such schemes, a computational process is responsible for signaling an end of a calculation by setting a halt bit, which needs to be systematically checked by an observer. ..."
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Classical models of computation traditionally resort to halting schemes in order to enquire about the state of a computation. In such schemes, a computational process is responsible for signaling an end of a calculation by setting a halt bit, which needs to be systematically checked by an observer. The capacity of quantum computational models to operate on a superposition of states requires an alternative approach. From a quantum perspective, any measurement of an equivalent halt qubit would have the potential to inherently interfere with the computation by provoking a random collapse amongst the states. This issue is exacerbated by undecidable problems such as the Entscheidungsproblem which require universal computational models, e.g. the classical Turing machine, to be able to proceed indefinitely. In this work we present an alternative view of quantum computation based on production system theory in conjunction with Grover’s amplitude amplification scheme that allows for (1) a detection of halt states without interfering with the final result of a computation; (2) the possibility of nonterminating computation and (3) an inherent speedup to occur during computations susceptible of parallelization. We discuss how such a strategy can be employed in order to simulate classical Turing machines. 1
Quantum Finite Automata, Quantum Pushdown Automata & Quantum Turing Machine: A Study
"... Abstract — An important question of quantum computing is that whether there is a computational gap between the models that is allowed to use quantum effect and a models that does not. Several types of Quantum computational models has been proposed including quantum finite automata, Quantum pushdown ..."
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Abstract — An important question of quantum computing is that whether there is a computational gap between the models that is allowed to use quantum effect and a models that does not. Several types of Quantum computational models has been proposed including quantum finite automata, Quantum pushdown Automata, Quantum branching programs. It has been shown that some computational models are more powerful than classical counterpart. In this paper we have compared the power among Quantum finite automata, pushdown Automata, turing machine.