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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.
  • It adds a 2007 reference point for readers tracking recent quantum research.
  • We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant.

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