Mile Gu et alii - How quantum physics could make 'The Matrix' more efficient @ Nature + Communications - Published 27 March 2012

Quantum simulations need to store less information to predict the future than do classical simulations. The finding applies to phenomena described by stochastic processes. Credit: Mile Gu / Center for Quantum Technologies at the National University of Singapore

Researchers have discovered a new way in which computers based on quantum physics could beat the performance of classical computers. The work, by researchers based in Singapore and the UK, implies that a Matrix-like simulation of reality would require less memory on a quantum computer than on a classical computer. It also hints at a way to investigate whether a deeper theory lies beneath quantum theory. The finding is published 27 March in Nature Communications.

The finding emerges from fundamental consideration of how much information is needed to predict the future. Mile Gu, Elisabeth Rieper and Vlatko Vedral at the Centre for  at the National Univesity of Singapore, with Karoline Wiesner from the University of Bristol, UK, considered the simulation of "stochastic" processes, where there are several possible outcomes to a given procedure, each occurring with a calculable probability. Many phenomena, from stock market movements to the diffusion of gases, can be modelled as stochastic processes.
The details of how to simulate such processes have long occupied researchers. The minimum amount of information required to simulate a given stochastic process is a significant topic of study in the field of complexity theory, where it is known in scientific literature as statistical complexity.
Researchers know how to calculate the amount of information transferred inherently in any stochastic process. Theoretically, this sets the lowest amount of information needed to simulate the process. In reality, however, classical simulations of stochastic processes require more storage than this.
Gu, Wiesner, Rieper and Vedral, who is also affiliated with the University of Oxford, UK, showed that quantum simulators need to store less information than the optimal classical simulators. That is because quantum simulations can encode information about the probabilities in a "superposition", where one of information can represent more than one classical bit.
What surprised the researchers is that the quantum simulations are still not as efficient as they could be: they still have to store more information than the process would seem to need.
That suggests  might not yet be optimized. "What's fascinating to us is that there is still a gap. It makes you think, maybe here's a way of thinking about a theory beyond ," says Vedral.
More information: For further details, see "Quantum mechanics can reduce the complexity of classical models" Nature Communications, 3, 762 (2012).http://www.nature. … mms1761.html

"Mathematical models are an essential component of quantitative science. They generate predictions about the future, based on information available in the present. In the spirit of simpler is better; should two models make identical predictions, the one that requires less input is preferred. Yet, for almost all stochastic processes, even the provably optimal classical models waste information. The amount of input information they demand exceeds the amount of predictive information they output. Here we show how to systematically construct quantum models that break this classical bound, and that the system of minimal entropy that simulates such processes must necessarily feature quantum dynamics. This indicates that many observed phenomena could be significantly simpler than classically possible should quantum effects be involved. (...)"