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How smooth is quantum complexity?
- Source :
- Journal of High Energy Physics; Oct2021, Vol. 2021 Issue 10, p1-19, 19p
- Publication Year :
- 2021
-
Abstract
- The "quantum complexity" of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical computational complexity, it has since been argued to hold a fundamental significance in its own right, as a physical quantity analogous to the thermodynamic entropy. In this paper, we present a unified perspective on various notions of quantum complexity, viewed as functions on the space of unitary operators. One striking feature of these functions is that they can exhibit non-smooth and even fractal behaviour. We use ideas from Diophantine approximation theory and sub-Riemannian geometry to rigorously quantify this lack of smoothness. Implications for the physical meaning of quantum complexity are discussed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 11266708
- Volume :
- 2021
- Issue :
- 10
- Database :
- Complementary Index
- Journal :
- Journal of High Energy Physics
- Publication Type :
- Academic Journal
- Accession number :
- 153620250
- Full Text :
- https://doi.org/10.1007/JHEP10(2021)230