Image by Kim Taylor for Quanta Magazine

Maybe most of you are not aware that we were happily living in an Einstein-Friedmann space-time until 1998. Hubble’s law had convinced us of the gentle character of a calm, quietly expanding universe, millions of galaxies running away from each other, kindly making up new empty space to be filled with the remaining interstellar gas. All the matter of the universe, hydrogen and helium produced in the first big boom… sorry, bang… 13,7 billions of years ago, would be used up over an infinitely long time, to make many beautiful new stars and galaxies, with absolutely no need to hurry. The only big question left open was about the rate of expansion: would the universe continue to grow indefinitely, although at a progressively slower velocity; or it would pass through a zero speed at some time, and then inevitably start to crunch back into a single point? 

Then, two independent teams had the strange idea of measuring the brightness of a particular type of exploding stars, the supernovae of type-I. For reasons that would take too long to explain in this simpleton letter, such stars have a well-defined, fixed value of maximum luminosity, the moment they will die in a sudden thermonuclear explosion. From the reduction in observed luminosity one can deduce their distance, and at the same time the redshift of their spectral lines allows us to deduce their velocity. The unsettling revelation of the supernova measurements was that the universe expansion was accelerating. This finding has changed our model of the Einstein-Friedmann universe into a desolating De Sitter landscape, in which solid matter and energy progressively dilute into nothingness, and dark matter dominates. It has blundered the social standing of science, and astrophysics in particular, admitting that we know only 5% of the universe and can only make a miserable guess about the remaining 95% unknown. And has upset our entire sense of life: how to bear the psychological pressure of living in a constantly accelerating condition? Can we still stop the world and get off, with Groucho Marx?

The De Sitter space-time was obtained in 1917 as a solution to Einstein’s equations for the case of an empty universe (as if our sense of loneliness was not enough already). The intrinsic curvature of spacetime in the absence of any matter or energy was modeled by the famous cosmological constant, Λ, which Einstein later called “my biggest blunder”. This corresponds to the vacuum having a positive energy density, and the positive cosmological constant gives a positive curvature to space, like the surface of a sphere. Einstein trashed this solution after the discovery of the expansion of the universe, and the 1922 version of the expanding space-time contained in Friedmann’s solution of the equations, with Λ=0, was accepted as the best fit to the observations. Until 1998, when Dark Energy and its companion Dark Matter made the constant Λ to strike back, resulting in the Λ-CDM or “standard cosmological model”, as the astrophysicists call it (should we still believe them?), of an ominously accelerating universe. And, as in the story of Dr. Jekyll and mr. Hyde, De Sitter can evoke also his evil double, an anti-De Sitter space-time. This would be perfectly similar to the former, except with the sign of the space-time curvature changed. In the anti-de Sitter space-time, in the absence of matter or energy, the cosmological constant is negative and the curvature looks like surface of a hyperbola. In such a weird(er) universe, empty space has negative energy density but positive pressure. Objects shrink as they move outward from the center of the space, becoming infinitesimal at the outer boundaries.

Now, you may ask, is this anti-De Sitter stuff of any relevance, beyond the academically elegant but useless playing with equations? As it turns out, anti-de Sitter (or AdS) space has nothing to do with gravity, but some theorists believe it to correspond to other forces in quantum mechanics, like electromagnetism, the weak and the strong nuclear forces. This is called the AdS/CFT correspondence, where CFT stands for “conformal field theory”. The idea was proposed around 1997 by Juan Maldacena, and later elaborated by Witten, Polyakov, Susskind and others. The original paper by Maldacena has more than 22,000 citations (that is more than twice per day, but as we know, there are too many high-energy theorists than available data, hence the mountain of self-citing papers which unduly boost their h-factors…) Such attempts at marrying quantum field theories and gravity have spurred a little interest in some models of nuclear and condensed matter physics, although no unified quantum gravity model is yet at the door (and not even in the waiting room). 

One relevant implication of the AdS/CFT correspondence was identified in a work by Maldacena and Susskind (MS), which found its origin in a neglected 1935 paper by Einstein and Rosen. ER (for short) had introduced the strange objects that we call today ‘wormholes’, while attempting to extend general relativity into a description not only of space-time, but of the subatomic particles that inhabit it. To make their particle picture work, ER took the singularities of the earliest Schwarzschild solution (the ‘black hole’) and replaced its sharp boundary with an extra-dimensional tube sliding to another part of space-time. ER argued that these ‘bridges’ (or wormholes) might represent particles. Their solution was wrong, but it contained the germs of another idea. So, MS started from the observation that general relativity contains such solutions in which two distant black holes are connected through a wormhole, or ER-bridge. And they made the bold supposition that these solutions can be interpreted as maximally entangled states of the two black holes. In this way, they made the analogy with the other famous paper by the Einstein-Podolsky-Rosen team, or EPR: the two black holes now formed a complex EPR-pair, just like two entangled photon or spin states. This was called the ER=EPR conjecture. In essence, this work established a new theoretical link between the worlds of gravity and quantum physics. MS speculated that the duality might be more general than that: it is very tempting to think that any EPR-correlated system may be connected by some sort of ER bridge. It was a very daring and poetic idea. Maybe Einstein’s guess that wormholes have to do with particles was right. Eventually.

It has long been understood that the two effects do not give rise to violations of the locality principle. One cannot use EPR correlations to send information faster than the speed of light. Similarly, ER bridges do not allow to send a signal from one asymptotic region to the other. This is sometimes stated by saying that wormholes are not traversable. This state of things started to change in 2015, when Alexei Kitaev showed that a particular quantum model of interacting particles could be made mathematically equivalent to a black hole in an anti-De Sitter space. In 2017, Jafferis, Gao and Wall used this concept to realize a traversable wormhole. They designed an AdS scenario in which negative repulsive energy holds a wormhole open long enough for something to pass from one end to the other. They also showed that such a gravitational description of a traversable wormhole is equivalent to quantum teleportation. It took another two years to construct a practical prescription to design a real quantum system: two groups of interacting particles connected by entanglement (representing the wormhole, according to the ER=EPR conjecture), and a qubit teleported from one group to the other. 

I hope you are still following the story, from Friedmann universe, to accelerating De Sitter universe, to its evil partner anti-De Sitter, to the AdS/CFT correspondence, to the ER=EPR conjecture that wormholes are equivalent to entanglement, to the traversable wormhole in an AdS-world, to its mapping into a quantum system of entangled groups of particles. What now? Enter Google’s Sycamore quantum computer. Maria Spiropolou, at Harvard, convinced Jafferis and people at Google to try to use a quantum computer to do quantum gravity experiments. The smallest version of the two-group-wormhole system would be encoded by seven qubits: 14 matter particle quantum states, split into two groups of 7, in which each particle of one group is entangled with one particle in the other. An eighth qubit is coupled to one group, let’s say the left one. The entangled quantum state initially spreads the information on the whole system of qubits. To generate the “negative energy” pulse that keeps the wormhole open, the spins of the seven qubits are simultaneously flipped. This makes the quantum state of the eighth qubit to localize on the right group of particles, thus performing the teleportation across the wormhole. Actually, quantum teleportation has been experimentally realized already several times, and in very different systems. What is important to understand here, is that quantum teleportation was realized between two special quantum systems that are mathematically equivalent to black holes in a virtual AdS space-time. Their paper Traversable wormhole dynamics on a quantum processor, with Jafferis as first author and Spiropoulou as the last, was published in the December 2022 issue of Nature. This would make a first experimental proof of the ER=EPR conjecture: space-time points connected by a wormhole are equivalent to entangled systems of particles. If this is proved, then also the reverse should be true: the geometry of space-time and gravity are determined by quantum entanglement of particles and radiation? 

Of course, critics say, this cannot be a realistic model of quantum gravity, for several reasons. For one, the De Sitter space-time of our (current picture of the) universe differs categorically from the anti-De Sitter: AdS has an outer boundary, onto which the quantum states can be projected (this also links with the holography concept, which I have no more space-time to describe here), while De Sitter space-time has no boundary, so there is no smooth mathematical transition that could possibly morph one into the other. Other critics noted that the ‘simple’ wormhole experiment concerns 2D space-time, the wormhole is just a filament with one spatial dimension plus the time dimension, whereas real gravity works in the 4D space-time that we actually live in, and is just a little bit more complex. However, one cannot help but thinking that such connections, even if too vague at times and too simplistic and undetermined at other times, between cosmology and gravity, quantum states and quantum information, black holes and wormholes, and the like, may be full of curiously interesting consequences. Sometimes I wonder what directions would I chose, if I were a young student of physics in these days… Wild and exciting? Or too much confusing? (Well, I still think I would end up in biophysics… but my reasons are complicated :))

Gravity in a quantum computer

Post navigation

Leave a Reply

Your email address will not be published. Required fields are marked *