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Curated by RSF Research Staff

Is spacetime a quantum code?

In 2014, physicists found evidence of a deep connection between quantum error correction and the nature of space, time and gravity. Generally, gravity is defined as the fabric of space and time but beyond Einstein’s theory, there must be a quantum origin from which the space-time somehow emerges.

The three physicists at the origin of this discovery, Ahmed Almheiri, Xi Dong and Daniel Harlow, suggested that a holographic “emergence” of space-time works just like a quantum error-correcting code. In their paper “Bulk Locality and Quantum Error Correction in AdS/CFT” published in its first version in November 2014, they showed that space-time emerges from this quantum error correction code in an anti-de Sitter (AdS) universes.

The discovery is opening a new way to capture more properties of space-time.

From left: Ahmed Almheiri, Xi Dong and Daniel Harlow originated a powerful new idea that the fabric of space-time is a quantum error-correcting code.

Their main idea was to consider a virtual universe called “anti-de Sitter space” (AdS) working like a hologram. In this representation, space-time in the interior of the universe is a projection that emerges from entangled quantum particles present on its outer boundary. AdS space is well known to physicists thanks to Juan Maldacena who proposed the anti-de Sitter/conformal field theory correspondence (AdS/CFT) that space-time is “holographically dual” to a quantum theory of particles living on the lower-dimensional, gravity-free boundary.

However, AdS universe is not intuitive. In our life, we experience a de Sitter space-time geometry and it’s different from an AdS space. One main difference is that our universe is infused with positive vacuum energy that causes it to expand without bound, while anti-de Sitter space has negative vacuum energy. Also, AdS space shares many key properties with a de Sitter world and it’s simpler to study. Both space-time geometries abide by Einstein’s theory; they simply curve in different directions. And more importantly, both kinds of universes contain black holes.

The most fundamental property of gravity is that there are black holes. That’s what makes gravity different from all the other forces. That’s why quantum gravity is hard.

- Daniel Harlow, assistant professor of physics at the Massachusetts Institute of Technology.

Quantum error correction explains how space-time achieves its “intrinsic robustness,” despite being woven out of fragile quantum stuff. It protects information by store it not in individual qubits, but in patterns of entanglement among many. The best error-correcting codes can typically recover all of the encoded information from slightly more than half of your physical qubits, even if the rest are corrupted. With space-time, the same correction seems to exist so, any point in the interior of AdS space could be constructed from slightly more than half of the boundary — just as in an optimal quantum error-correcting code. Everything inside a region of the interior space-time called the “entanglement wedge” can be reconstructed from qubits on an adjacent region of the boundary.

We’re not walking on eggshells to make sure we don’t make the geometry fall apart. I think this connection with quantum error correction is the deepest explanation we have for why that’s the case.

- John Preskill, a theoretical physicist at the California Institute of Technology

And in 2018, Almheiri expanded the theory to the black holes in a new article “Holographic Quantum Error Correction and the Projected Black Hole Interior”. The theory enables to probe the mysteries of black holes. It appears quantum error correction is “essential for maintaining the smoothness of space-time at the horizon” of a two-mouthed black hole, called a wormhole. Quantum error correction, as well as preventing firewalls, also explains how qubits escape a black hole after falling in, through strands of entanglement between the inside and outside that are themselves like miniature wormholes. This could resolve Hawking’s paradox.

Everything traces back to black holes. These paradox-ridden places are where gravity reaches its zenith and Einstein’s general relativity theory fails. [..] There are some indications that if you understand which code space-time implements, it might help us in understanding the black hole interior.

- Ahmed Almheiri, a theoretical physicist the Institute for Advanced Study in Princeton, New Jersey

The language of quantum error correction is providing a new way of describing black holes. The presence of a black hole is defined by the breakdown of correctability,”.

When there are so many errors that you can no longer keep track of what’s going on in the bulk [space-time] anymore, you get a black hole. It’s like a sink for your ignorance. It’s really entanglement which is holding the space together. If you want to weave space-time together out of little pieces, you have to entangle them in the right way. And the right way is to build a quantum error-correcting code.

RSF—in perspective

These new developments are going in the same direction as Nassim Haramein researches suggesting that space-time is much more than just an empty vacuum.


By Dr. Olivier Alirol, RSF Research Scientist

Read more at:

Quantamagazine: How Space and Time Could Be a Quantum Error-Correcting Code  Bulk Locality and Quantum Error Correction in AdS/CFT


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