Quantum information theory: Quantum complexity grows linearly for an exponentially long time.
Physicists know about the huge chasm between quantum physics and the theory of gravity. However, in recent decades, theoretical physics has provided some plausible conjecture to bridge this gap and to describe the behavior of complex quantum many-body systems, for example black holes and wormholes in the universe. Now, a theory group at Freie Universität Berlin and HZB, together with Harvard University, USA, has proven a mathematical conjecture about the behavior of complexity in such systems, increasing the viability of this bridge. The work is published in Nature Physics.
“We have found a surprisingly simple solution to an important problem in physics,” says Prof. Jens Eisert, a theoretical physicist at Freie Universität Berlin and HZB. “Our results provide a solid basis for understanding the physical properties of chaotic quantum systems, from black holes to complex many-body systems,” Eisert adds.
Quantum Complexity and Many-Body Systems
Using only pen and paper, i.e. purely analytically, the Berlin physicists Jonas Haferkamp, Philippe Faist, Naga Kothakonda and Jens Eisert, together with Nicole Yunger Halpern (Harvard, now Maryland), have succeeded in proving a conjecture that has major implications for complex quantum many-body systems. “This plays a role, for example, when you want to describe the volume of black holes or even wormholes,” explains Jonas Haferkamp, PhD student in the team of Eisert and first author of the paper.
Complex quantum many-body systems can be reconstructed by circuits of so-called quantum bits. The question, however, is: how many elementary operations are needed to prepare the desired state? On the surface, it seems that this minimum number of operations — the complexity of the system — is always growing. Physicists Adam Brown and Leonard Susskind from Stanford University formulated this intuition as a mathematical conjecture: the quantum complexity of a many-particle system should first grow linearly for astronomically long times and then — for even longer — remain in a state of maximum complexity. Their conjecture was motivated by the behavior of theoretical wormholes, whose volume seems to grow linearly for an eternally long time. In fact, it is further conjectured that complexity and the volume of wormholes are one and the same quantity from two different perspectives. “This redundancy in description is also called the holographic principle and is an important approach to unifying quantum theory and gravity. Brown and Susskind’s conjecture on the growth of complexity can be seen as a plausibility check for ideas around the holographic principle,” explains Haferkamp.
A New Approach Combining Geometry and Quantum Information
The group has now shown that the quantum complexity of random circuits indeed increases linearly with time until it saturates at a point in time that is exponential to the system size. Such random circuits are a powerful model for the dynamics of many-body systems. The difficulty in proving the conjecture arises from the fact that it can hardly be ruled out that there are “shortcuts,” i.e. random circuits with much lower complexity than expected. “Our proof is a surprising combination of methods from geometry and those from quantum information theory. This new approach makes it possible to solve the conjecture for the vast majority of systems without having to tackle the notoriously difficult problem for individual states,” says Haferkamp.
“The work in Nature Physics is a nice highlight of my PhD,” adds the young physicist, who will take up a position at Harvard University at the end of the year. As a postdoc, he can continue his research there, preferably in the classic way with pen and paper and in exchange with the best minds in theoretical physics.
Reference: “Linear growth of quantum circuit complexity” by Jonas Haferkamp, Philippe Faist, Naga B. T. Kothakonda, Jens Eisert and Nicole Yunger Halpern, 28 March 2022, Nature Physics.
DOI: 10.1038/s41567-022-01539-6
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24 Comments
What wormholes? There are none that we know of, so using a theoretical, hypothetical object to “solve” anything is illogical. I don’t buy it at all.
Wormholes were not used to “solve” a problem here. They only helped motivate the researchers to think about a problem that needed proof. It turned out that this proof also helps explain things like black holes and may even help solve bigger problems like the connection between gravity and quantum mechanics. Whether wormholes exist or not is not that important; what is important is that they help researchers think about problems.
In other words, what the researchers did was add to the mathematical foundations of physics; doing this helps explain things that exist like black holes and things that may or may not exist, like wormholes or the link between gravity and quantum mechanics.
“What wormholes? There are none that we know of,…?”
Wasn’t so long ago that we didn’t know of any blackholes…and now we find them everywhere.
I’ll give you credit though. Even though he would do the math right up to where x/0, Einstein himself didn’t believe such a thing as a blackhole really existed.
-and yet they, indeed, do.
At the end of the Big Bang inflation when the universe became symmetrical there was an atom- foam cloud. That cloud had two energies repel each other. The gravity and fifth energy. The fifth energy split the foam from the atoms having them burnt and took them in its stream. Fifth energy collected itself after it was distributed within the cloud and the energy it repelled. By collecting itself it created a region of fifth energy and the burnt foam, against a region of gravity that has the visible matter. It is just like a swirl of a tornedo, but separate in its own region. Same principle applied on creating the galaxies. fifth energy trapped between visible matter, after that region created. small many regions of that trapped fifth energy started to form scattered between the visible matter. They grow until no more trapped fifth energy within the visible matter. They are like a tornedo swirl pulls itself from the gravity and visible matter region. There are no two different worlds they connect. They dont pull visible matter, only their trapped potentials, fifth energy is like a wind energy and behavior repel the gravity and vidible matter. originated from before the Big Bang. These scattered fifth energy regions later became the centers of galaxies when negative gravity created around them coming along with it toward the centers. Before that, there was positive gravity which the fifth energy repelled. It came along with the negative gravity toward the center of the swirl. This is the start of creating galaxies when no event horizon and singularity existed. They existed at the end of creating the galaxies. Now there is no atom- foam cloud, all atoms became part or inside galaxies, foam became part of the skies of the galaxies. In addition to the web that carries the filaments and walls in the universe. There is no wormholes connecting between two worlds, this is just a science fiction. Quantum could be involved because gravity and fifth energy are energies existed just prior to the start of the Big Bang.
You state this in a manner that is so matter of fact I can only assume you were there to witness it. So if I may ask, because this article doesn’t even mention it, what is gravity? How is it, that what we call gravity, causes everything on Earth to be so powerfully attracted to the Earth? As just one of the many questions that one might have about gravity.
Keep the faith
I think even Einstein and Heisenberg would be very challenged by these new mathematics of the universe.
… nice but…
i found a worm hole in my apple i was eating and it was gross meow.
Me too. I will buy a real computer next time and not some sort of fruit half eaten.
The conjecture applies to wormholes and blackholes. Indeed, we have not detected any wormhole yet but we did detect blackholes. You surely did not check the mathematical proof of this conjecture. So we reject your arguments for its lack of rigor.
Suppose that the maximally entangled and complex state is in conformity with Noether’s Symmetry Principle? 🤔
Infinite complexity deflates information. Perfect.
This article went over my head. Can many-body help me understand?
…und wir fallen alle mit Lichtgeschwindigkeit durch die Zeit in Richtung großer Massen wo die Zeit stoppt oder maximaler Entropie wo die Zeit stoppt….
The source for the force of gravity will never be found if the ramifications of the Big Bang theory continue to be considered facts. Examples? It is a fact that the universe is expanding. It is a fact gravity alone can create a star out of a mere cloud of gas. It is a fact supernovae exist.
The problem is, they aren’t facts. They are all part of the same theory which is the Big Bang, Lambda-CDM model. Science has convinced itself that all these smaller theories are facts to make the Big Bang theory itself a fact.
Our current theories make a mockery of science itself. Our universe, which contains 2 trillion galaxies of normal matter and the other 95% of the dark matter, was forced to back itself into a spot so small that scientists cannot even describe what it is. There are laws that keep this from being able to happen like the Planck law. Matter can only get so small. This directly relates to the first law of thermodynamics which states matter doesn’t get created or destroyed. Well, there will be some destroying of matter if the universe tried to go back where it came from.
Gravity is not understood because of the Big Bang theory so there will be no explanation for gravity until science is ready to do away with the Big Bang theory. The problem is what the theory thinks gravity is itself. A cloud of gas and dust must create its own gravity to make it become a star. This makes all the gravity the cloud creates only attributed to the normal matter itself. There will no need for space to create gravity at all so that is what happened because of the theory. Space became a property of our universe that doesn’t have anything to do with gravity. Unfortunately, Einstein said that space is curved to create gravity but that didn’t matter because the Big Bang theory became a law.
The answer to gravity is as simple as the article implies. Gravity did not create all the energy we see, a massive collision in space did. Our universe turned itself into a particle collider with two objects that contained the mass of the observable galaxies. Our universe did exactly what scientists do all the time in particle colliders. They create quark plasma shrapnel and our universe created quark plasma shrapnel as the galaxies.
The big bang theory thinks gravity comes before energy but it doesn’t. Gravity comes after energy. It takes energy to create gravity. The Big Bang theory had no energy to use in the early universe so gravity was chosen to do everything. The problem is that it was the collision that created the energy, not gravity. This is the theory that changes the role of gravity that will make it understandable.
Our universe is an extremely pressurized field of electron neutrinos. That is what space is made of. Heat in normal matter manipulates this field by creating electron neutrinos by destroying electrons with heat and shooting them from the mass gravitationally invisible. These outgoing particles push out on the natural pressure of space and cause gravitational lensing since it’s all made of the same matter. The natural pressure of space pushes through the outgoing matter and creates gravity for normal matter. These incoming neutrinos also form lightning as they reform into electrons in the ungrounded clouds. This is why lightning happens in all types of clouds.
The only thing that will make us understand gravity is a paradigm shift. To find it, everything thought to be facts needs to be considered a theory again.
Ahmad, if you wear your tinfoil hat next time, that sort of thing won’t happen.
Atoms have electrons in orbit and an orbit is a balance between gravitational pull and tangential velocity. Therefore, the nucleus of the atom has a gravitational force and it then follows than gravity of any mass is the totality of that pull of each atom.
This would apply to gas, liquid or solid so all of these have a gravitational force that would have those attracting particles to each other. The unknown then is what is the mechanism of the gravitational force of protons and neutrons?
it then follows that gravity of any mass is the totality of that pull of each atom.
… sorry, I was bit busy whit this thing>Lola Indigo – Tamagochi (Live Performance) | Vevo LIFT… WoW… it hits me bad, I am very bad with this ….
While I understood only about 10% of this article, I am comforted by the fact that the comments section displays the usual frothy mixture of paranoid fantasy, absolute certainty, and the requisite amount of snark in roughly equal measure.
But, as a layman, I can’t tell which one is valid enough to pay attention to, and which can be dismissed easily.
I would recommend either a) turning off comments for pieces like this, or b) institute some heavy moderation that can separate the wheat from the chaff.
Dr. Pollock,
Was there anything prior to the Big Bang?
Well Nathan Reed, I did try to address your question, but my answer I feel, may not sit within parameters set by scitech daily.com.
You had my reply but it has not appeared on the comments yet.
Your question was in fact, the only comment needing a response in my humble opinion.
It would interest me highly to hear from you.
Does no one believe in God anymore?
It’s surprising that most people want answers to unseen causes that produce effects on matter we can see. The answers may differ from star to star, let alone galaxies. Guys it’s beyond human comprehension, we are a part of this universe, but we will never own, or understand all of its complexities.
Believing in an original explosion to generate everything we understand today, frankly beggars belief.
What is so out of touch to believe life does exist out there in this vast universe, in the manner of a far superior life form, able to generate life?
It would be very interesting and I welcome your views on this please.