Optimal quantum computation linked to gravity

Optimal quantum computation linked to gravity
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Information and gravity may seem like completely different things, but one thing they have in common is that they can both be described in the framework of geometry. Building on this connection, a new paper suggests that the rules for optimal quantum computation are set by gravity.

Physicists Paweł Caputa at Kyoto University and Javier Magan at the Instituto Balseiro, Centro Atómico de Bariloche in Argentina have published their paper on the link between and gravity in a recent issue of Physical Review Letters.

In the field of , one of the main ideas is minimizing the cost (in terms of computational resources) to solve a problem. In 2006, Michael Nielsen demonstrated that, when viewed in the context of differential geometry, computational costs can be estimated by distances. This means that minimizing computational costs is equivalent to finding minimal "geodesics," which are the shortest possible distances between two points on a curved surface.

As this geometric perspective is very similar to the concepts used to describe gravity, Nielsen's results have led researchers to investigate possible connections between computational complexity and gravity. But the work is challenging, and researchers are still trying to figure out basic questions such as how to define "complexity" in holographic models related to , in particular, conformal field theory. Currently there are many different proposals for laying the foundations in this area.

The main purpose of the new paper is to bring these different ideas together by proposing a universal description of complexity that depends only on a single quantity (central charge). This leads to the discovery of connections between complexity and concepts in (quantum) gravity which, in turn, leads to interesting implications such as the possibility that gravity governs the rules for optimal quantum computation.

"Recently, quantum computation theorists (including Nielsen) put forward the idea that the complexity of quantum circuits can be estimated by the length of the shortest geodesic in the 'complexity geometry of unitary transformations,'" Caputa told Phys.org. "We showed that, in two-dimensional conformal field theories with quantum gates given by the energy-momentum tensor, the 'length' of such geodesics is computed by (the action of) two-dimensional gravity.

"Finding the minimal length on the complexity geometry, in our setup, is equivalent to solving the equations of gravity. This is what we meant by gravity setting rules for optimal computations in 2-D conformal field theories."

This perspective suggests that gravity could be useful in estimating computational complexity and identifying the most efficient computational methods for solving problems.

"The notion of complexity of a certain task tells us how difficult it is to perform it using our available tools," Magan said. "In the quantum theory of computation, this notion is generalized to the complexity of quantum circuits built out from quantum gates. Estimating it is in general a difficult problem.

"We showed that there are families of quantum systems where the complexity of certain universal tasks is well estimated using classical gravity (general relativity). Over the years, using holography and Anti-de Sitter/conformal field theories, we have been learning that gravity is intimately related to quantum information. The lesson from our findings is that may also teach us how to perform quantum in physical systems in the most efficient way."


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More information: Paweł Caputa and Javier M. Magan. "Quantum Computation as Gravity." Physical Review Letters. DOI: 10.1103/PhysRevLett.122.231302
Journal information: Physical Review Letters

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Citation: Optimal quantum computation linked to gravity (2019, June 28) retrieved 24 August 2019 from https://phys.org/news/2019-06-optimal-quantum-linked-gravity.html
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Jun 28, 2019
Yet four-dimensional cosmological censor ship is still upheld when conditioning function on reduction and not unitarity. As analytic continuation shows, there is a singularity of a degree of freedom. Whether this is SU(1) or SU(3) remains and open question. Nature as subtle as she is, does not have to be the 11-dimensional mean. SU(3) mapped without an ontological SO(2), may not represent unbound SU(2) and yet it too is exclusive of certain configurations of ontological representation. We should not exclude othonormality, yet it is too simple to accept. We should not exclude isotropy for the need of distinguish-ability, but then such a free degree is held. The return of but one chosen from PCT due to free parameters leads the far side of flop back to the serene, but the accident is the prior of dimensiality. It seems reciprocity cannot do it without the integers.
The tipping point being, work or complexity. Accidental substrate or psychologically effective, but still useful? Modal.

Jun 28, 2019
So.... where are ya goin' with that?
Seems you've discovered a world of esoteric jargonality...

Jun 28, 2019
The idea isn't new, see perspective piece
https://www.ucl.a...fall.pdf
on Nielsen's paper, which is shared on his site here:
http://michaelnie...2070.pdf Looks like these researchers are building on that..

It's pretty sexy to me, I know some about computation complexity and less about physics, but my favorite physics was from Feynman lectures, being shown how straight line and incident angle off mirror, classic optics, emerges out of sum of probability amplitudes. Quantum basis of path of least action. Scott Aaronson has given good layman descriptions of Shor's algorithm, saying it works similar way, and now this work.., smells like quantum programs can possibly compute their own optimal design? Wow!

Then there's the other angle, the universe acting like a simulation and doing laziest computations, here gravity is laziest bc Information maps to energy transfer
https://en.m.wiki...rinciple

Jun 28, 2019
The notion in the article is interesting. Light seems to 'solve' for the least energy path in a gravity field (because it always follows a geodesic). in effect it follows the path of least action.

Jun 28, 2019
Is the use of the term "quantum gravity" appropriate in this sense - if it is does it imply that there's a linkage between quantum computation and the quantum structure of reality; or have we all been reading too much greg egan?:)

Jun 28, 2019
38years later you are all still purguring and plagarising my work.
All those non disclosures still doing there Job Anti ?

Jun 29, 2019
38years later you are all still purguring and plagarising my work.
All those non disclosures still doing there Job Anti ?

Your attention to detail (spelling, in this case) is a strong indicator of any work you might have done in the past...

Jun 29, 2019
Yet four-dimensional cosmological censor ship is still upheld


Does that word salad has anymore tangible references than last time when orbital momentum made you spout off tangent about orbifolds?

Computer science lies - due to its treatment of computational resources near enough physics to be interesting. So let us discuss the article instead.

Jun 29, 2019
Is the use of the term "quantum gravity" appropriate in this sense - if it is does it imply that there's a linkage between quantum computation and the quantum structure of reality


Good question! Since they are trying to incorporate the holographic principle - likely to make modeling simpler - it is not necessarily so, we do not know that it applies even for an AdS universe, which we are not. More interesting is the resource (time, likely) minimization part of geodesics, but those too crop up in dynamical models by necessity.

Say, being a bioinformatician I note that the branching physics of phylogenetic (population relationships) trees not surprisingly emulates light cone physics. I.e. both have hyperbolic geometry of geodesic distance measurements. But that does not *mean* anything in relation to the underlying physics, it is just inherent in branching. So CS and physical action both tries to minimize time (or distance), but that is just by design respectively by nature.

Jun 29, 2019
Is the use of the term "quantum gravity" appropriate in this sense - if it is does it imply that there's a linkage between quantum computation and the quantum structure of reality


Good question!


ER = EPR. Carry on.

Jun 29, 2019
Some people think wormholes make more sense than allowing gravitational information flows to be retro-reflective and baryon-centric at low noise energy levels. As I disagree it seems to me the gravitational energy exchanges of detector and source nuclei can support nonlocal hidden variable effects without having information exceeding light-speed. GR supports a lot of strange notions because static gravity fields involve no mass-to-mass exchanges of gravity carriers, meaning static gravity effects lack gravitons, no support for hidden variables synchronizing effects at both ends of a channel.

Jun 29, 2019
So the question is ...

How do you transport a lighter 1C^3 particle into or through a heavier gravity space ?

If a proton weight particle emits a photon it will pop straight up to the 1C^3 weight, if you want to exchange the photon between heavier particles a 3d-space mono-weight-dimensionaly directed gravity-space tensor is your only option.

Jun 30, 2019
When humans understand a higher math called influential numbers and create a device to be able to see the energy fields... Only then they will understand that gravity itself has a polarity and many other attributes related to energy fields now not yet seen.

Yes we will travel without fuels and engines. All the learned people commenting above do not have the tools to understand much... They have a lot to unlearn .

Jul 02, 2019
sigh.
when will they learn that gravity is not a property of geometry

Jul 08, 2019
I don't claim to have a clear understanding of the above article but For those of you who are interested in physics, you might really like to see ion thruster that can lift its power supply from the ground!.. It took a huge increase in thrust to weight ratio to do it!...Please google "Self Contained Ion Powered Aircraft," to see it fly.

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