| Autor: |
Vir B. Bulchandani, S. L. Sondhi |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Journal of High Energy Physics, Vol 2021, Iss 10, Pp 1-19 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
1029-8479 |
| DOI: |
10.1007/JHEP10(2021)230 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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