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Quantum Algorithms: Philosophical Lessons

Abstract

I discuss the philosophical implications that the rising new science of quantum computing may have on the philosophy of computer science. While quantum algorithms leave the notion of Turing-Computability intact, they may re-describe the abstract space of computational complexity theory hence militate against the autonomous character of some of the concepts and categories of computer science.

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Fig. 1

Notes

  1. It is noteworthy that it is exactly this problem of scaling that, so far, prevents the realization of a quantum computer. In contrast, other aspects of quantum information theory, namely quantum communication and quantum cryptography, are very near technological realization.

  2. Unitarity requires that \(\forall k \neq k^{\prime}:\; _A\langle{a_k}\vert{a_{k^{\prime}}}\rangle_A=0\).

  3. The quantum adiabatic algorithm (Farhi et al. 2000) may give us similar results, contingent upon the existence of an energy gap that decreases polynomially with the size of the input.

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Hagar, A. Quantum Algorithms: Philosophical Lessons. Minds & Machines 17, 233–247 (2007). https://doi.org/10.1007/s11023-007-9057-3

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Keywords

  • Quantum computing
  • Computational complexity
  • The Church-Turing thesis