Here shows that single-precision is almost always enough. Therefore, if you want to calculate open quantum system dynamics by numerically calculating the appropriate Feynman integral, the last diagram The same paper showed that single-precision and double-precision gave almost the same result for every version of the problem except the ones in which the influence of the noise was very strong (rapid loss of quantum coherence in the system of interest):
![turing fp64 turing fp64](https://www.gamersnexus.net/images/media/2018/gpus/2080-ti/arch/sm-architecture-block-diagram.jpg)
You can see in the figure below that the speed-up gained by using the GPU also increased with the amount of RAM that the calculation required (the RAM required can increase depending on the size of the system, for example) up to about a 20x speed-up, but since the figure below was done prior to May 2012 I couldn't go beyond 4GB on the GPU! I can only imagine what this would look like now in 2022: The program accomplishes this by calculating the appropriate double Feynman integral numerically, and more details can be found in this answer at Quantum Computing Stack Exchange.Īs long as the GPU has enough RAM, the calculation is much faster on a GPU than a CPU, and this difference increases as you try to simulate the system dynamics for more and more picoseconds (all figures below come from my 2013 paper about the software, which is called "FeynDyn" since is uses the Feynman integral to calculate dynamics):
#Turing fp64 software
I wrote a software to "exact quantum dynamics" calculations, meaning that given a density matrix of a system under the influence of noise at one point in time, the program gives you the quantum mechanical time-evolution of the density matrix with no semi-classical, Markovian, weak-coupling, or other physical approximations, as long as you give the program the temperature and the Hamiltonian describing the system and the noise from its environment.