Space and Time Could Be a Quantum Error-Correcting Code

Ignorance invariably abounds when it comes to black hole interiors. Stephen Hawking’s 1974 epiphany that black holes radiate heat, and thus eventually evaporate away, triggered the infamous “black hole information paradox,” which asks what happens to all the information that black holes swallow. Physicists need a quantum theory of gravity to understand how things that fall in black holes also get out. The issue may relate to cosmology and the birth of the universe, since expansion out of a Big Bang singularity is much like gravitational collapse into a black hole in reverse.


AdS space simplifies the information question. Since the boundary of an AdS universe is holographically dual to everything in it—black holes and all—the information that falls into a black hole is guaranteed never to be lost; it’s always holographically encoded on the universe’s boundary. Calculations suggest that to reconstruct information about a black hole’s interior from qubits on the boundary, you need access to entangled qubits throughout roughly three-quarters of the boundary. “Slightly more than half is not sufficient anymore,” Almheiri said. He added that the need for three-quarters seems to say something important about quantum gravity, but why that fraction comes up “is still an open question.”

In Almheiri’s first claim to fame in 2012, the tall, thin Emirati physicist and three collaborators deepened the information paradox. Their reasoning suggested that information might be prevented from ever falling into a black hole in the first place, by a “firewall” at the black hole’s event horizon.

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Like most physicists, Almheiri doesn’t really believe black hole firewalls exist, but finding the way around them has proved difficult. Now, he thinks quantum error correction is what stops firewalls from forming, by protecting information even as it crosses black hole horizons. In his latest, solo work, which appeared in October, he reported that quantum error correction is “essential for maintaining the smoothness of space-time at the horizon” of a two-mouthed black hole, called a wormhole. He speculates that quantum error correction, as well as preventing firewalls, is also 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 would resolve Hawking’s paradox.

This year, the Department of Defense is funding research into holographic space-time, at least partly in case advances there might spin off more efficient error-correcting codes for quantum computers.

On the physics side, it remains to be seen whether de Sitter universes like ours can be described holographically, in terms of qubits and codes. “The whole connection is known for a world that is manifestly not our world,” Aaronson said. In a paper last summer, Dong, who is now at the University of California, Santa Barbara, and his co-authors Eva Silverstein and Gonzalo Torroba took a step in the de Sitter direction, with an attempt at a primitive holographic description. Researchers are still studying that particular proposal, but Preskill thinks the language of quantum error correction will ultimately carry over to actual space-time.

“It’s really entanglement which is holding the space together,” he said. “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.”

Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

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