Theoretical Physicists Shed Light on Quantum Complexity Using Gravitational Twists

The answer to the question ‘Are we are living in a computer simulation?’ can be found hiding in an unusual quantum phenomenon which occurs in metals as a reaction to twists of space-time geometry.

Artistic impression of a space-time twist in a crystal. (CREDIT -Oxford University)

A repeated theme in science fiction, most notably popularized by the "Matrix' film trilogy, is whether man’s physical reality is a computer simulation. While this appears to be a rather philosophical notion, in theoretical physics it has a fascinating twist when applied to computer simulations of multifaceted quantum systems.

How can one even try to answer that question? In new research published in Science Advances magazine, a team of Theoretical Physicists from the University of Oxford and the Hebrew University may have discovered a way to answer it.

Researchers Zohar Ringel and Dmitry Kovrizhin while attempting to address a computer simulation of a quantum phenomenon occurring in metals found evidence that such a simulation is impossible as a matter of principle. More precisely, they presented how the complexity of this simulation - that can be measured in a number of processor hours, electricity bills, and memory size - increases in line with the number of particles one would have to mimic.

If the quantity of computational resources required for a quantum simulation increases gradually (e.g. linearly) with the number of particles in the system, then one has to double the number of processors, memory, etc. so as to be able to mimic a system twice as large in the same amount of time. But if the growth is exponential, or in other words if for every additional particle one has to double the number of processors, memory, etc., then this mission becomes intractable. Keep in mind that even just to store the information about a few hundred electrons on a computer one would need a memory assembled from more atoms than there are in the Universe.

The Researchers identified a specific physical occurrence that cannot be captured by any local quantum: Monte-Carlo simulation. It is an interesting effect, which has been around for years, but has only ever been measured indirectly. In the field of condensed matter physics, it is referred to as the "thermal Hall conductance" and in high-energy physics it is termed as a "gravitational anomaly".

Simply put, thermal Hall conductance denotes a generation of energy currents in the direction transverse to either temperature gradient, or a twist in the underlying geometry of space-time. A number of physical systems in high magnetic fields and at very low temperatures are thought to display this effect. Interestingly such quantum systems have been dodging efficient numerical simulation algorithms for years.

In their research, the Theorists revealed that for systems displaying gravitational anomalies the quantities which are involved in quantum Monte-Carlo simulations will obtain a negative sign or become complex. This spoils the effectiveness of the Monte-Carlo method through what is referred to as "the sign-problem". Locating a solution to "the sign problem" would make large-scale quantum simulations possible, so that the proof that this issue cannot be solved for certain systems is a crucial one.

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 genuine quantum effect: one for which no local classical analogue exists.

Zohar Ringel, Professor, Hebrew University, and Co-author of the paper

This research also offers an encouraging message to Theoretical Physicists. It is regularly said in society that machines are replacing people leading to a takeover of human jobs. For instance, in the event that someone develops a computer powerful enough to mimic all the properties of large quantum systems in the blink of an eye. Obviously the appeal of hiring a Theoretical Physicist to perform precisely the same job (with the overhead considerations of office space, pension, travel money etc.) would be significantly reduced.

But, should Theoretical Physicists be worried by this likelihood? On the bright side, there are a number of critical and interesting quantum systems, some associated to high-temperature superconductivity, and others linked to topological quantum computation, for which no efficient simulation algorithms are identified.

On the other hand, maybe such algorithms are only waiting to be discovered? Professor Ringel and Kovrizhin contend that, when it comes to a physically significant subset of complex quantum data, a class of algorithms as wide as Monte-Carlo algorithms cannot outwit them and are not expected to in the near future.

In the context of the initial question of whether man’s perceived reality is truly just a part of a radical alien experiment, this research may provide additional reassurance to some of us.

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