Turing machines based on unsharp quantum logic
نویسندگان
چکیده
In this paper, we consider Turing machines based on unsharp quantum logic. For a lattice-ordered quantum multiple-valued (MV) algebra E , we introduce E -valued non-deterministic Turing machines (E NTMs) and E -valued deterministic Turing machines (E DTMs). We discuss different E valued recursively enumerable languages from width-first and depth-first recognition. We find that width-first recognition is equal to or less than depth-first recognition in general. The equivalence requires an underlying E value lattice to degenerate into an MV algebra. We also study variants of E NTMs. E NTMs with a classical initial state and E NTMs with a classical final state have the same power as E NTMs with quantum initial and final states. In particular, the latter can be simulated by E NTMs with classical transitions under a certain condition. Using these findings, we prove that E NTMs are not equivalent to E DTMs and that E NTMs are more powerful than E DTMs. This is a notable difference from the classical Turing machines.
منابع مشابه
The computing power of Turing machine based on quantum logic
Super-Turing computational power has been invoked by models of computation that make use of new physical principles or of different underlying logic of computation. Recently, it has been observed that Turing machines based on quantum logic can solve undecidable problems. In this paper we will give recursion-theoretical characterization of the computational power of this kind of quantum Turing m...
متن کاملUniversality and programmability of quantum computers
Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a finite number of qubits. The problem of universality has been addressed most famously in a paper by Deutsch, and later by Ber...
متن کاملQuantum Algorithms, Paraconsistent Computation and Deutsch's Problem
We present the new model of paraconsistent Turing machines and revise the models of quantum Turing machines and quantum circuits, stressing the concepts of entangled states and quantum parallelism which are important features for efficient quantum algorithms. We revise a quantum circuit that solves the so-called Deutsch’s problem, and then provide another solution to Deutsch’s problem by means ...
متن کاملSome improvements in fuzzy turing machines
In this paper, we improve some previous definitions of fuzzy-type Turing machines to obtain degrees of accepting and rejecting in a computational manner. We apply a BFS-based search method and some level’s upper bounds to propose a computational process in calculating degrees of accepting and rejecting. Next, we introduce the class of Extended Fuzzy Turing Machines equipped with indeterminacy s...
متن کامل