Algorithmic information theory
Algorithmic information theory
Hilbert's tenth problem
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Computing with cells and atoms: an introduction to quantum, DNA and membrane computing
Computing with cells and atoms: an introduction to quantum, DNA and membrane computing
Quantum computation and quantum information
Quantum computation and quantum information
Elements of the Theory of Computation
Elements of the Theory of Computation
Hypercomputation with quantum adiabatic processes
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
Hypercomputation: philosophical issues
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
Minds and Machines
Quantum Algorithms: Philosophical Lessons
Minds and Machines
Physical Computation: How General are Gandy's Principles for Mechanisms?
Minds and Machines
On the Possibilities of Hypercomputing Supertasks
Minds and Machines
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We explore the possibility of using quantum mechanical principles for hypercomputation through the consideration of a quantum algorithm for computing the Turing halting problem. The mathematical noncomputability is compensated by the measurability of the values of quantum observables and of the probability distributions for these values. Some previous no-go claims against quantum hypercomputation are then reviewed in the light of this new positive proposal.