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The Quantum Challenge to Structural Complexity Theory (1992)
| Citations: | 53 - 4 self |
BibTeX
@MISC{Berthiaume92thequantum,
author = {Andre Berthiaume and Gilles Brassard},
title = {The Quantum Challenge to Structural Complexity Theory},
year = {1992}
}
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Abstract
This is a non-technical survey paper of recent quantum-mechanical discoveries that challenge generally accepted complexity-theoretic versions of the Church--Turing thesis. In particular, building on pionering work of David Deutsch and Richard Jozsa, we construct an oracle relative to which there exists a set that can be recognized in Quantum Polynomial Time (QP), yet any Turing machine that recognizes it would require exponential time even if allowed to be probabilistic, provided that errors are not tolerated. In particular, QP 6` ZPP relative to this oracle. Furthermore, there are cryptographic tasks that are demonstrably impossible to implement with unlimited computing power probabilistic interactive Turing machines, yet they can be implemented even in practice by quantum mechanical apparatus. 1 Deutsch's Quantum Computer In a bold paper published in the Proceedings of the Royal Society, David Deutsch put forth in 1985 the quantum computer [7] (see also [8]). Even though this may c...
Keyphrases
quantum challenge structural complexity theory quantum computer david deutsch non-technical survey paper royal society cryptographic task quantum polynomial time quantum mechanical apparatus exponential time richard jozsa oracle relative turing machine power probabilistic interactive turing machine bold paper church turing thesis complexity-theoretic version recent quantum-mechanical discovery
