# Making a Dual of a Traversable Wormhole with a Quantum Computer

November 30, 2022

Posted by Alexander Zlokapa, Student Researcher, and Hartmut Neven, VP of Engineering, Quantum AI Team

Wormholes — wrinkles in the fabric of spacetime that connect two disparate locations — may seem like the stuff of science fiction. But whether or not they exist in reality, studying these hypothetical objects could be the key to making concrete the tantalizing link between information and matter that has bedeviled physicists for decades.

Surprisingly, a quantum computer is an ideal platform to investigate this connection. The trick is to use a correspondence called AdS/CFT, which establishes an equivalence between a theory that describes gravity and spacetime (and wormholes) in a fictional world with a special geometry (AdS) to a quantum theory that does not contain gravity at all (CFT).

In “Traversable wormhole dynamics on a quantum processor”, published in *Nature* today, we report on a collaboration with researchers at Caltech, Harvard, MIT, and Fermilab to simulate the CFT on the Google Sycamore processor. By studying this quantum theory on the processor, we are able to leverage the AdS/CFT correspondence to probe the dynamics of a quantum system equivalent to a wormhole in a model of gravity. The Google Sycamore processor is among the first to have the fidelity needed to carry out this experiment.

## Background: It from Qubit

The AdS/CFT correspondence was discovered at the end of a series of inquiries arising from the question: What’s the maximum amount of information that can fit in a single region of space? If one asked an engineer how much information could possibly be stored in a datacenter the answer would likely be that it depends on the number and type of memory chips inside it. But surprisingly, what is inside the data center is ultimately irrelevant. If one were to cram more and more memory chips with denser and denser electronics into the datacenter then it will eventually collapse into a black hole and disappear behind an event horizon.

When physicists such as Jacob Bekenstein and Stephen Hawking tried to compute the information content of a black hole, they found to their surprise that it is given by the area of the event horizon — not by the volume of the black hole. It looks as if the information inside the black hole was written on the event horizon. Specifically, a black hole with an event horizon that can be tiled with *A* tiny units of area (each unit, called a “Planck area,” is 2.6121×10^{−70} m^{2}) has at most *A*/4 bits of information. This limit is known as the Bekenstein-Hawking bound.

This discovery that the maximum amount of information that could fit in a region was proportional not to its volume, but to the surface area of the region’s boundary hinted at an intriguing relationship between quantum information and the three-dimensional spatial world of our everyday experience. This relationship has been epitomized by the phrase “It from qubit,” describing how matter (“it”) emerges from quantum information (“qubit”).

While formalizing such a relationship is difficult for ordinary spacetime, recent research has led to remarkable progress with a hypothetical universe with hyperbolic geometry known as “anti-de Sitter space” in which the theory of quantum gravity is more naturally constructed. In anti-de Sitter space, the description of a volume of space with gravity acting in it can be thought of as encoded on the boundary enclosing the volume: every object inside the space has a corresponding description on the boundary and vice versa. This correspondence of information is called the holographic principle, which is a general principle inspired by Bekenstein and Hawking's observations.

Schematic representation of anti-de Sitter space (interior of cylinder) and its dual representation as quantum information on the boundary (surface of cylinder). |

The AdS/CFT correspondence allows physicists to connect objects in space with specific ensembles of interacting qubits on the surface. That is, each region of the boundary encodes (in quantum information) the content of a region in spacetime such that matter at any given location can be "constructed" from the quantum information. This allows quantum processors to work directly with qubits while providing insights into spacetime physics. By carefully defining the parameters of the quantum computer to emulate a given model, we can look at black holes, or even go further and look at two black holes connected to each other — a configuration known as a wormhole, or an Einstein-Rosen bridge.

## Experiment: Quantum Gravity in the Lab

Implementing these ideas on a Sycamore processor, we have constructed a quantum system that is dual to a traversable wormhole. Translated from the language of quantum information to spacetime physics via the holographic principle, the experiment let a particle fall into one side of a wormhole and observed it emerging on the other side.

Traversable wormholes were recently shown to be possible by Daniel Jafferis, Ping Gao and Aron Wall. While wormholes have long been a staple of science fiction, there are many possible spacetime geometries in which the formation of a wormhole is possible, but a naïvely constructed one would collapse on a particle traveling through it. The authors showed that a shockwave — i.e., a deformation of spacetime that propagates at the speed of light — of negative energy would solve this problem, propping open the wormhole long enough to enable traversability. The presence of negative energy in a traversable wormhole is similar to negative energy in the Casimir effect, where vacuum energy pushes together closely spaced plates. In both cases, quantum mechanics permits the energy density at a given location in space to be either positive or negative. On the other hand, if the wormhole experienced a shockwave of *positive* energy, no information would be allowed to pass through.

The simplest application of the holographic principle to create a wormhole requires many, many qubits — in fact, to approach the pencil-and-paper solutions given by theoretical physicists, one would need an arbitrarily large number of qubits. As the number of qubits is reduced, additional corrections are required that are still poorly understood today. New ideas were needed to build a traversable wormhole on a quantum computer with a limited number of qubits.

One of us (Zlokapa) adopted ideas from deep learning to design a small quantum system that preserved key aspects of gravitational physics. Neural networks are trained via backpropagation, a method that optimizes parameters by directly computing the gradient through the layers of the network. To improve the performance of a neural network and prevent it from overfitting to the training dataset, machine learning (ML) practitioners employ a host of techniques. One of these, sparsification, attempts to restrict the detail of information in the network by setting as many weights as possible to zero.

Similarly, to create the wormhole, we started with a large quantum system and treated it like a neural network. Backpropagation updated the parameters of the system in order to maintain gravitational properties while sparsification reduced the size of the system. We applied ML to learn a system that preserved only one key gravitational signature: the importance of using a negative energy shockwave. The training dataset compared dynamics of a particle traversing a wormhole propped open with negative energy and collapsed with positive energy. By ensuring the learned system preserved this asymmetry, we obtained a sparse model consistent with wormhole dynamics.

Learning procedure to produce a sparse quantum system that captures gravitational dynamics. A single coupling consists of all six possible connections between a given group of four fermions. |

Working with Jafferis and a handful of collaborators from Caltech, Fermilab, and Harvard, we subjected the new quantum system to numerous tests to determine if it showed gravitational behavior beyond signatures induced by different energy shockwaves. For example, while quantum mechanical effects can transmit information across a quantum system in a diverse set of ways, information that travels in spacetime — including through a wormhole — must be causally consistent. This and other signatures were verified on classical computers, confirming that the dynamics of the quantum system were consistent with a gravitational interpretation as viewed through the dictionary of the holographic principle.

Implementing the traversable wormhole as an experiment on a quantum processor is an extraordinarily delicate process. The microscopic mechanism of information transfer across qubits is highly chaotic: imagine an ink drop swirling in water. As a particle falls into a wormhole, its information gets smeared over the entire quantum system in the holographic picture. For the negative energy shockwave to work, the scrambling of information must follow a particular pattern known as perfect size winding. After the particle hits the negative energy shockwave, the chaotic patterns effectively proceed in reverse: when the particle emerges from the wormhole, it is as if the ink drop has come back together by exactly undoing its original turbulent spread. If, at any point in time, a small error occurs, the chaotic dynamics will not undo themselves, and the particle will not make it through the wormhole.

On the Sycamore quantum processor, we measured how much quantum information passed from one side of the system to the other when applying a negative versus a positive energy shockwave. We observed a slight asymmetry between the two energies, showing the key signature of a traversable wormhole. Due to the protocol’s sensitivity to noise, the Sycamore processor’s low error rates were critical to measuring the signal; with even 1.5x the amount of noise, the signal would have been entirely obscured.

## Looking Forward

As quantum devices continue to improve, lower error rates and larger chips will allow deeper probes of gravitational phenomena. Unlike experiments such as LIGO that record data about gravity in the world around us, quantum computers provide a tool to explore theories of quantum gravity. We hope that quantum computers will help develop our understanding of future theories of quantum gravity beyond current models.

Gravity is only one example of the unique ability of quantum computers to probe complex physical theories: quantum processors can provide insight into time crystals, quantum chaos, and chemistry. Our work demonstrating wormhole dynamics represents a step towards discovering fundamental physics using quantum processors at Google Quantum AI.

You can also read more about this result here.

## Acknowledgements

*We would like to thank our Quantum Science Communicator Katherine McCormick for her help writing this blog post.*

**Update — 2023/02/17:**We updated the title of this blog post to more accurately reflect the technical contribution of our work.