Square root of ‘not’: a major difference between fuzzy and quantum logics. (English) Zbl 1231.03027
Summary: Many authors have mentioned the similarity between quantum logic and fuzzy logic. In this paper, we show that, in spite of this similarity, these logics are not identical. Specifically, we emphasize that, while quantum logic has a special ‘square root of not’ operation, which is very useful in quantum computing, fuzzy logic lacks such an operation.
References:
| [1] | Cormen T.H., Introduction to algorithms (2001) · Zbl 1047.68161 |
| [2] | Dalla Chiara M.L., Reasoning in quantum theory: sharp and unsharp quantum logics (2004) · Zbl 1059.81003 |
| [3] | DOI: 10.1142/S0219749905000943 · Zbl 1075.81015 · doi:10.1142/S0219749905000943 |
| [4] | DOI: 10.1007/s11225-007-9079-0 · Zbl 1127.06008 · doi:10.1007/s11225-007-9079-0 |
| [5] | Grover, L., 1996. A fast quantum mechanical algorithm for database search. In: Proceeding of 28th ACM symposium on theory of computing, 212–219 · Zbl 0922.68044 |
| [6] | DOI: 10.1103/PhysRevLett.79.325 · doi:10.1103/PhysRevLett.79.325 |
| [7] | DOI: 10.1103/PhysRevLett.80.4329 · doi:10.1103/PhysRevLett.80.4329 |
| [8] | Klir G., Fuzzy sets and fuzzy logic: theory and applications (1995) · Zbl 0915.03001 |
| [9] | Kosko B., Fuzzy thinking: the new science of fuzzy logic (1993) · Zbl 0782.94005 |
| [10] | Nguyen H.T., First course in fuzzy logic (2006) |
| [11] | Nielsen M.A., Quantum computation and quantum information (2000) · Zbl 1049.81015 |
| [12] | Seising, R. From principles of mechanics to quantum mechanics – a survey on fuzziness in scientific theories. In: Proceedings of the 27th international conference of the North American fuzzy information processing society NAFIPS’2008, New York, May 19–22 |
| [13] | Shor, P., 1994. Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th annual IEEE symposium on foundations of computer science, 124–134 |
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