Margolus-Levitin theorem

In the theory of quantum computers, the Margolus-Levitin theorem describes the fundamental physical limit of the speed of state changes and thus indirectly the computing power of a computer. It was derived from Norman Margolus and Lev B. Levitin .

The limit is around 3 × 10 ³³ operations per second per joule . The limit results from considering the unitary evolution of a closed quantum system in an initially pure state.

 Ein Quantensystem der Energie  ${\displaystyle E}$ benötigt mindestens die Zeit  ${\displaystyle {\frac {h}{4E}}}$ um zwischen zwei zueinander orthogonalen Zuständen zu wechseln.

Here is the Planck's constant and denotes the average energy above the ground state , that is, the energy expectation value in the initial state, minus the energy ground state. ${\displaystyle h}$ ${\displaystyle E}$

The theorem is also of interest in other branches of physics, for example through its connection with the holographic principle or to find limits for information processing in the context of black holes , and was also used to estimate the total computing capacity of the universe.

The Margolus-Levitin theorem can be interpreted as a “quantum speed limit” for information processing. Generalizations of this limit (e.g. for the non-unitary dynamics of open quantum systems or other measures of distinctness than orthogonality) are still the subject of current research.

See also

• Energy-time uncertainty relation

literature

• Norman Margolus and Lev B. Levitin: The maximum speed of dynamical evolution . In: Physica D . tape 120 , 1998, pp. 188-195 , doi : 10.1016 / S0167-2789 (98) 00054-2 , arxiv : quant-ph / 9710043 (English).
• LI Mandelshtam and IE Tamm : The uncertainty relation between energy and time in nonrelativistic quantum mechanics . In: J. Phys. (USSR) . tape 9 , 1945, p. 249–254 (English, narod.ru [PDF; accessed January 5, 2017] Russian original: Izv. Akad. Nauk SSSR (ser. Fiz.) 9, 122–128 (1945)).

Individual evidence

1. ^ Norman Margolus and Lev B. Levitin: The maximum speed of dynamical evolution . In: Physica D . tape 120 , 1998, pp. 188-195 , doi : 10.1016 / S0167-2789 (98) 00054-2 , arxiv : quant-ph / 9710043 (English).
2. ↑ Stephen DH Hsu: Physical limits on information processing . In: Physics Letters B . tape 641 , no. 1 , September 28, 2006, p. 99-100 , doi : 10.1016 / j.physletb.2006.08.018 (English).
3. ^ Seth Lloyd , Y. Jack Ng: Black Hole Computers . In: Scientific American . tape 4 , April 1, 2007 (English, scientificamerican.com [accessed January 5, 2017]).
4. ^ Seth Lloyd : Computational capacity of the universe . In: Phys. Rev. Lett . tape 88 , 2002, p. 237901 , doi : 10.1103 / PhysRevLett.88.237901 , arxiv : quant-ph / 0110141 (English).
5. ^ A. del Campo, IL Egusquiza, MB Plenio , Susanna F. Huelga: Quantum speed limits in open system dynamics . In: Phys. Rev. Lett. tape 110 , p. 050403 , doi : 10.1103 / PhysRevLett.110.050403 , arxiv : 1209.1737 (English).
6. ↑ Diego Paiva Pires, Marco Cianciaruso, Lucas C. Céleri, Gerardo Adesso and Diogo O. Soares-Pinto: Generalized Geometric Quantum Speed ​​Limits . In: Phys. Rev. X . tape 6 , June 2, 2016, p. 021031 , doi : 10.1103 / PhysRevX.6.021031 , arxiv : 1507.05848 (English).