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Quantum Simulation
On the Quantum Kolmogorov Complexity of Classical Strings
arXiv
Authors: Markus Mueller
Year
2007
Paper ID
49624
Status
Preprint
Abstract Read
~2 min
Abstract Words
99
Citations
N/A
Abstract
We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant. Both complexities are defined as the minimal length of any (classical resp. quantum) computer program that outputs the corresponding string. It follows that quantum complexity is an extension of classical complexity to the domain of quantum states. This is true even if we allow a small probabilistic error in the quantum computer's output. We outline a mathematical proof of this statement, based on an inequality for outputs of quantum operations and a classical program for the simulation of a universal quantum computer.
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- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant.
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