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IRREVERSIBILITY IN THE HALTING PROBLEM OF QUANTUM COMPUTER

Alexander Shalyt-Margolin, В. И. Стражев, A. Ya. Tregubovich

The Halting problem of a quantum computer is considered. It is shown that if halting of a quantum computer takes place the associated dynamics is described by an irreversible operator.

arXiv:quant-ph/0106108Modern Physics Letters BJul 10, 20071 citation

The halting problem for universal quantum computers

Tien D. Kieu, Michael Danos

The halting of universal quantum computers is shown to be incompatible with the constraint of unitarity of the dynamics.

arXiv:quant-ph/9811001Nov 2, 19984 citations

Remarks on the undecidability of the quantum halting problem

Daegene Song

The halting problem is a decision problem first posed and proved by Alan Turing in 1936. With the recent surge of interest in quantum computation, one is led to ask if the problem can also be considered for a quantum computer. It is reported that the halting problem may not be solved consistently in both the Schrodinger and Heisenberg pictures of quantum dynamics. The assumption of the existence of the quantum halting machine leads to a contradiction when a vector representing an observable is the system that is to be unitarily evolved in both pictures.The halting problem is a decision problem first posed and proved by Alan Turing in 1936. With the recent surge of interest in quantum computation, one is led to ask if the problem can also be considered for a quantum computer. It is reported that the halting problem may not be solved consistently in both the Schrodinger and Heisenberg pictures of quantum dynamics. The assumption of the existence of the quantum halting machine leads to a contradiction when a vector representing an observable is the system that is to be unitarily evolved in both pictures.

Jan 22, 20071 citation

Unsolvability of the Halting Problem in Quantum Dynamics

Song, D

It is shown that the halting problem cannot be solved consistently in both the Schrodinger and Heisenberg pictures of quantum dynamics. The existence of the halting machine, which is assumed from quantum theory, leads into a contradiction when we consider the case when the observer's reference frame is the system that is to be evolved in both pictures. We then show that in order to include the evolution of observer's reference frame in a physically sensible way, the Heisenberg picture with time going backwards yields a correct description.It is shown that the halting problem cannot be solved consistently in both the Schrodinger and Heisenberg pictures of quantum dynamics. The existence of the halting machine, which is assumed from quantum theory, leads into a contradiction when we consider the case when the observer's reference frame is the system that is to be evolved in both pictures. We then show that in order to include the evolution of observer's reference frame in a physically sensible way, the Heisenberg picture with time going backwards yields a correct description.

Oct 7, 20067 citations

The Halting Problem for Quantum Computers

Noah Linden, Sandu Popescu

We argue that the halting problem for quantum computers which was first raised by Myers, is by no means solved, as has been claimed recently. We explicitly demonstrate the difficulties that arise in a quantum computer when different branches of the computation halt at different, unknown, times.

arXiv:quant-ph/9806054Jun 16, 199824 citations

Quantum recursion theory

Karl Svozil

Incompleteness and undecidability theorems have to be revised in view of quantum information and computation theory. qrt.tex 1 As has already been pointed out in Gödel’s centennial paper on the incompleteness af arithmetic [1], the classical undecidability theorems of formal logic [2] and the theory of computable functions [4, 5] are based on semantical pardoxes such as the liar [6] or Richard’s paradox. The method of diagonalization, which was first applied by Cantor for a proof of the undenumerability of real numbers [7], has been applied by Turing for a proof of the recursive undecidability of the halting problem [8]. The halting problem is the problem of whether or not an arbitrary algorithm terminates or produces a particular output and terminates. Assume that the halting problem is decidable. Turing [8] proved that this assumption yields a contradiction. To construct the contradiction, considerIncompleteness and undecidability theorems have to be revised in view of quantum information and computation theory. qrt.tex 1 As has already been pointed out in Gödel’s centennial paper on the incompleteness af arithmetic [1], the classical undecidability theorems of formal logic [2] and the theory of computable functions [4, 5] are based on semantical pardoxes such as the liar [6] or Richard’s paradox. The method of diagonalization, which was first applied by Cantor for a proof of the undenumerability of real numbers [7], has been applied by Turing for a proof of the recursive undecidability of the halting problem [8]. The halting problem is the problem of whether or not an arbitrary algorithm terminates or produces a particular output and terminates. Assume that the halting problem is decidable. Turing [8] proved that this assumption yields a contradiction. To construct the contradiction, consider

arXiv:hep-th/9412048Dec 6, 19944 citations

Remarks on the Halting problem, unitarity and reversibility in quantum theory of computations

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Remarks on the Halting problem, unitarity and reversibility in quantum theory of computations

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