Gravitational twists help theoretical physicists shed light on quantum complexity

Artistic impression of a space-time twist in a crystal. Credit: University of Oxford

Are we living in a computer simulation? Curiously, the crux of this question may be hiding in an exotic quantum phenomenon that appears in metals in response to twists in spacetime geometry.

A recurring theme in science fiction, popularized by the “Matrix” movie trilogy, is whether our physical reality is a computer simulation. Although this seems like a rather philosophical idea, in theoretical physics it has an interesting twist when applied to the computer. simulations of complex quantum systems.

How can we even attempt to answer this question? In new research published in Scientists progress magazine, a team of theoretical physicists from Oxford University and Hebrew University, may have found a way to address this answer.

In trying to approach a computer simulation of a quantum phenomenon occurring in metals, the researchers, Zohar Ringel and Dmitry Kovrizhin, found evidence that such a simulation is impossible in principle. Specifically, they showed how the complexity of this simulation, which is measured in CPU hours, memory size and electricity bills, increases with the number of particles that would need to be simulated.

If the amount of computational resources required for a quantum simulation increases slowly (e.g. linearly) with the number of particles in the system, then the number of processors, memory, etc. must be doubled. in order to be able to simulate a system twice as large in the same amount of time. But if the growth is exponential, that is to say if for each additional particle we must double the number of processors, memory, etc., then this task becomes insoluble. Note that even to store the information of a few hundred electrons on a computer would require a memory built from more atoms than there are in the Universe.

The researchers identified a particular physical phenomenon that cannot be captured by any local quantum: the Monte Carlo simulation. This is a curious effect, known for decades, but which has only ever been measured indirectly. In the field of condensed matter physics it is called “thermal Hall conductance” and in high energy physics it is called a “gravitational anomaly”.

Clearly, Hall thermal conductance involves a generation of energy currents in the direction transverse to either temperature gradient, or a twist in the underlying geometry of spacetime. Many physical systems in high magnetic fields and at very low temperatures are believed to exhibit this effect. Interestingly, these quantum systems have eluded effective numerical simulation algorithms for decades.

In their work, the theorists have shown that for systems with gravitational anomalies, the quantities involved in quantum Monte Carlo simulations will take on a negative sign or become complex. This ruins the effectiveness of the Monte Carlo approach through what is called “the sign problem”. Finding a solution to the “sign problem” would make large-scale quantum simulations possible, so proof that this problem cannot be solved for some systems is important.

“Our work provides an intriguing link between two seemingly unrelated topics: gravitational anomalies and computational complexity. It also shows that the thermal Hall conductance is a true quantum effect: an effect for which there is no local classical analogue,” says Zohar Ringel, professor at Hebrew University and co-author of the paper.

This work also brings a reassuring message to theoretical physicists. It is often said in society that machines are taking the place of people and will eventually take over human jobs. For example, in the event that someone, for example, creates a computer powerful enough to simulate all the properties of large quantum systems, in the blink of an eye. Clearly the appeal of hiring a theoretical physicist to do exactly the same job (with the general considerations of office space, travel money, pension, etc.) would be greatly diminished.

But should theoretical physicists be alarmed by this possibility? On the bright side, there are many important and interesting quantum systems, some related to high-temperature superconductivity and others related to topological quantum computing, for which no efficient simulation algorithm is known. On the other hand, maybe such algorithms are just waiting to be discovered? Professor Ringel and Kovrizhin argue that when dealing with a physically large subset of complex quantum data, a class of algorithms as broad as Monte Carlo algorithms, cannot and cannot outsmart us. probably won’t in the near future.

In the context of the original question of whether our perceived reality is really just part of an advanced extraterrestrial experience, this work may reassure some of us.

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More information:
“Quantized gravitational responses, sign problem and quantum complexity” Scientists progress (2017).

Provided by Oxford University

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