10,000 times faster calculations of many-body quantum dynamics possible:
A team led by Professor Michael Bonitz from the Institute of Theoretical Physics and Astrophysics at Kiel University (CAU) has now succeeded in developing a simulation method, which enables quantum mechanical calculations up to around 10,000 times faster than previously possible. They have published their findings in the current issue of the renowned scientific journal Physical Review Letters.
The new procedure of the Kiel researchers is based on one of the currently most powerful and versatile simulation techniques for quantum mechanical many-body systems.
It uses the method of so-called nonequilibrium Green functions: this allows movements and complex interactions of electrons to be described with very high accuracy, even for an extended period.
[...] to date this method is very computer-intensive: in order to predict the development of the quantum system over a ten times longer period, a computer requires a thousand times more processing time.
With the mathematical trick of introducing an additional auxiliary variable, the physicists at the CAU have now succeeded in reformulating the primary equations of nonequilibrium Green functions such that the calculation time only increases linearly with the process duration.
[...] The new calculation model of the Kiel research team not only saves expensive computing time, but also allows for simulations, which have previously been completely impossible. "We were surprised ourselves that this dramatic acceleration can also be demonstrated in practical applications," explained Bonitz.
Original publication:
Niclas Schlünzen, Jan-Philip Joost, Michael Bonitz, Achieving the Scaling Limit for Nonequilibrium Green Functions Simulations, Physical Review Letters 124, 7, (2020) DOI: 10.1103/PhysRevLett.124.076601
https://link.aps.org/doi/10.1103/PhysRevLett.124.076601
(Score: 2, Informative) by Anonymous Coward on Tuesday February 25 2020, @11:27AM (4 children)
Reading between the journalist's lines of incompetence ("10,000 times as fast"), the scientists managed to take an algorithm with a computational complexity of O(n^3) down to O(n). That is no mean feat! And a great boon to all users, surely.
(Score: 0) by Anonymous Coward on Tuesday February 25 2020, @11:44AM (2 children)
How is the journalist's description inaccurate?
(Score: 2) by Common Joe on Tuesday February 25 2020, @11:55AM (1 child)
The grandparent already explained that -- it's going from exponential down to linear computation. His information seems to come from this line:
Thus, I agree with grandparent. It seems it goes from O(n^3) down to O(n).
(Score: 0) by Anonymous Coward on Tuesday February 25 2020, @01:27PM
nitpick. it's polynomial in both cases. 3rd order polynomial decreases to 1st order polynomial.
exponential would be O(2^n) (or some other basis).
(Score: 0) by Anonymous Coward on Tuesday February 25 2020, @03:17PM
Really good stuff. Though it looks like they're building on an improvement of O(n^2) from the original. It should be noted these aren't exact solutions and there appear to be (acceptable) accuracy tradeoffs, but still huge wins.
(Score: 1, Troll) by pkrasimirov on Tuesday February 25 2020, @12:12PM
Break trough the discrete logarithm problem, therefore assymetric encryption, therefore SSL, therefore encrypted data and digital signatures. Combine with Deepfake audio and video. Stir with coronaviruses. Mod me troll.
(Score: 2) by hendrikboom on Tuesday February 25 2020, @01:10PM
I guess this is this century's mathematics. I remember last century, a mathematician studying string theory said that string theory was next century's mathematics. Well, it's the next century now. I'm looking forward to more of this.