Traversable wormhole dynamics on a quantum processor
Nature DOI: 10.1038/s41586-022-05424-3 (live November 30 2022 16:00 UTC)
Daniel Jafferis, Alexander Zlokapa, Joseph D. Lykken, David K. Kolchmeyer, Samantha I. Davis, Nikolai Lauk, Hartmut Neven, and Maria Spiropulu
Image credit: inqnet/A. Mueller
Wondros Podcast with the authors
Jafferis Dec 4 2022 Princeton talk (https://phy.princeton.edu/symposium-and-workshop-program)
Plain English Summary
In 2015, Alexei Kitaev showed that a simple quantum dynamical system of fermions, called the Sachdev-Ye-Kitaev (SYK) model, exhibits an explicit “holographic duality,” meaning that it has quantum dynamics that look like quantum gravity effects in an emergent space. This suggests the possibility of doing quantum gravity experiments on quantum processors.
In 2019, Gao and Jafferis showed that by entangling two SYK models, one should be able to perform “wormhole teleportation,” producing and measuring the dynamical properties expected of a traversable wormhole in an emergent space. A wormhole (as coined by John Wheeler) is an Einstein-Rosen bridge between two remote spacetime regions. In the general theory of relativity, nothing is allowed to pass through a wormhole if positive and negative energy fluctuations are balanced. As shown by Gao, Jafferis, and Wall in 2016, a negative energy shockwave can prop the wormhole open and enable traversability. Hawking in 1975 already pointed out that Hawking radiation from a black hole, as viewed by a fiducial observer near the horizon, also looks like pulses of negative energy going into the black hole.
A team of physicists realized this type of wormhole dynamics experimentally on a quantum device at Google, namely the Sycamore quantum processor. Using quantum gates, the team inserted a qubit into one SYK-like system and observed the information emerging from the other SYK-like system on the same quantum processor. The dynamics of the process are seen to be consistent with behavior expected from a quantum system dual to a wormhole in a two dimensional anti-de Sitter (AdS) spacetime. These dynamics nominally would require a quantum system with an arbitrarily large number of fermions — i.e., an arbitrarily large number of qubits in an experiment. As the number of fermions is reduced, the resulting gravitational behavior becomes less well-understood from a theoretical perspective due to corrections from string theory. Although it is difficult to a-priori write down a quantum system that resembles gravity when queried through the dictionary of “holographic duality”, the team employed learning techniques to find such a small and simple quantum system that could be encoded in the current quantum architectures and that would preserve the gravitational properties.
The quantum system produced by learning techniques and was subjected to a suite of additional checks. In this work, the physicists report on behavior expected both from the perspective of gravity and from quantum information. For example, while quantum mechanical effects can transmit information across a quantum system in a variety of ways, causal time-ordering of events must be satisfied if information spreading through a quantum system is dual to signals traveling through spacetime. The team shows that if the wormhole is propped open for long enough time by the negative energy shockwaves, a causal path is established between the two SYK quantum systems. They verified these and other properties with classical computer calculations.
On the Sycamore processor, they measured how much quantum information passed from one SYK system to the other when applying a negative versus a positive energy shockwave. More quantum information was transferred when a negative energy shockwave was used — i.e., the observed dynamics were consistent with the quantum system being dual to a traversable wormhole. Due to the sensitivity of the protocol to noise, the high fidelity of the quantum processor used was essential. For example, if the error rates were higher by 50%, the signal would have been entirely obscured. If the error rates were half, about ten times the signal would be observed.
The work constitutes a step towards a larger program of probing gravitational physics using a quantum computer. It does not substitute for direct probes of quantum gravity in the same way as other planned future experiments that might probe quantum gravity effects in the future using quantum sensing, but it does offer a powerful testbed to exercise ideas of quantum gravity
Traversable Wormhole Protocol
We discuss the quantum circuit that describes a particle traversing a wormhole in the holographic dual. Throughout the following steps, we require a quantum system (referred to by physicists as a “Hamiltonian”, the microscopic description of the system) denoted by H. Only some systems H are dual to gravity; the SYK model is an example of H known by theoretical physicists to have a gravitational dual. In this work, through a learning process that begins with an SYK model the researchers devised a new SYK-like system H with gravitational properties. Once a small enough system, and still dual to gravity is identified, the following protocol is known to be equivalent to traversing a wormhole.
- Prepare an entangled state between two copies of H: one is the left side of the wormhole, and the other is the right side of the wormhole. This entangled state is dual to a wormhole at time t=0. The devised through learning small SYK-like system has 7 Majorana fermions on the left and 7 Majorana fermions on the right; encoding all 14 fermions in superconducting qubits requires 7 qubits.
- Evolve the wormhole backwards in time according to H. This moves the horizons of the left and right mouths of the wormhole.
- Prepare two maximally entangled qubits: call one the “reference” qubit and the other the “probe” qubit. We later attempt to send the probe qubit through the wormhole, and we will be able to check if it made it through by comparing against the reference qubit. These two additional qubits bring the total circuit size to 9 qubits.
- Swap the probe qubit with one of the qubits in the left quantum system of the wormhole. This inserts the entanglement probe qubit into the wormhole.
- Evolve the wormhole forwards in time according to H. As this happens, the information of the probe qubit gets chaotically scrambled throughout the entire quantum system.
- Apply an entangling interaction between the two sides of the wormhole. In the gravitational dual, this corresponds to sending an energy shockwave through spacetime. We can apply an interaction that gives this shockwave negative energy to prop open the wormhole and make it traversable, or we can choose a positive energy shockwave to close the wormhole and prevent information from getting across.
- Evolve the wormhole forwards in time according to H. As this happens, information of the probe qubit undergoes further chaotic dynamics. The dynamics refocus the information onto the right side of the wormhole.
- Measure the amount of entanglement between the rightmost qubit of the right system and the reference qubit. More entanglement means more information was transferred from the left system to the right system. In our experiment, we observed more entanglement when a negative energy shockwave was used compared to a positive energy shockwave, which is consistent with the interpretation that some quantum information was transferred via the traversable wormhole mechanism.
Glossary
holographic principle/duality
A dictionary, developed by Juan Maldacena of IAS Princeton and other theoretical physicists, that translates between 1) physics in a special type of spacetime with gravity and 2) a quantum system without gravity but with quantum entanglement. A quantum system is said to be “dual” to a spacetime configuration when the two settings describe equivalent physics. The special type of spacetime is called anti-de Sitter space (AdS); unlike the ordinary spacetime we live in, the anti-de Sitter space has constant negative curvature.
N.B. For the quantum system implemented in this work, which can be referred to as ‘baby’ SYK-like, the exact gravitational dual is not known; nonetheless the dynamics and properties of the quantum system are consistent with the existence of a gravitational dual.
ER=EPR conjecture
Conjecture by theoretical physicists Lenny Susskind of Stanford and Juan Maldacena of IAS, Princeton (2013) that wormholes are equivalent to quantum entanglement. The conjecture is that wormholes and quantum physics, specifically entanglement (a phenomenon in which two particles can remain connected across vast distances), may have a connection. The physicists speculated that wormholes (or “ER”) were equivalent to entanglement (also known as “EPR” after Albert Einstein, Boris Podolsky, and Nathan Rosen in works of the previous century (1935)).
holographic wormhole / traversable wormhole
A bridge between two regions of spacetime in a special model of spacetime (anti-de Sitter space), such that a particle can enter one side of the wormhole and emerge on the other side of the wormhole. Not all wormholes are traversable; a particle that enters a non-traversable wormhole will not emerge on the other side. The only wormholes known to be traversable are also described by a dual quantum system (in our case the so-called SYK quantum system) via the holographic principle.
quantum gravity
A theory of gravity that describes gravitational phenomena in the language of quantum mechanics.
quantum processor
A chip consisting of qubits that implements physical interactions between the qubits to realize quantum mechanical effeccts.
qubit
A quantum generalization of the classical bit (0 or 1). It is described by a superposition of 0 and 1 states with a quantum mechanical relative phase between the two states.
SYK model
A quantum system consisting of coupled Majorana fermions with random coupling strengths. In our experiment, we use an SYK-like model since it has couplings that are learned instead of randomized. Named after physicists Alexei Kitaev, Subir Sachdev and Jinwu Ye. 1,2,3
Q&A
Q: What is a wormhole in plain terms? Did the team create a rupture in space-time in this experiment?
A: A wormhole (coined by John Wheeler) is a theoretical spacetime bridge between two remote regions in the universe. Such wormholes are consistent with Einstein’s theory of general relativity but they have not been seen or observed experimentally. In their simplest configuration, wormholes do not allow anything to go through them: they are not traversable.
No, in this experiment no rupture of spacetime was created in the hardware of physical space. A traversable wormhole was deduced to have emerged based on quantum information being teleported using quantum codes on the quantum processor.
Q: Can you explain the role of classical computing in the quantum gravity “baby” model you constructed?
A: To find a small quantum system that has gravitational properties, we used techniques from machine learning. This required a classical computer to run simulations and produce candidate quantum systems that were thought to preserve gravitational dynamics. The team then ran further simulations and checks on classical computers to identify gravitational behavior. Given a quantum computer with lower error rates, all learning techniques and additional simulations could be run more efficiently using a quantum computer.
Q: In the paper the team refers to this as a quantum experiment rather than a quantum simulation. Can you explain? Is this a probe of quantum gravity, say, like LHC probes supersymmetry?
A: The team calls this a “quantum experiment” because they prepared a highly entangled system and directly measured observables of the physical system. One can “simulate” the system on a conventional computer, and indeed this was done as reported in this paper, no physical system is created in a conventional simulation which is the manipulation of classical bits (zeros and ones). Using the term “quantum experiment” instead of “quantum simulation” highlights this difference. The quantum system the team realized is theorized to be dual to gravitational behavior according to a theory of quantum gravity in a different type of spacetime than ours (the AdS). This is entirely different from experiments at the LHC, which produce and measure the naturally occurring physics of our surrounding world.
History
A section of important theoretical history developments from the 20th and especially 21st century relevant to this work will be added here. There is a massive theoretical engine of ingenuity that this works rests upon. Come back soon to read about it.
Possible misunderstandings of “Traversable wormhole dynamics on a quantum processor” including technical/nomenclature clarifications
Q: Did we claim to have produced or observed a wormhole deformation of 3+1-dimensional spacetime?
A: No.
Q: What did we observe?
A: We observed phenomena produced by the Sycamore quantum processor that are consistent with the dynamics of a traversable wormhole. The observed phenomena can be equally well characterized as a particular form of quantum teleportation. The fact that there are two seemingly equivalent descriptions is consistent with the ER=EPR hypothesis of Maldacena and Susskind.
Q: Was this a simulation then?
A: It is conventional to call any process on a digital or analog quantum device a “quantum simulation”, so we do not object to this characterization. However, there is a crucial difference between a classical simulation (on a conventional computer) of quantum teleportation versus a quantum teleportation protocol on a quantum processor. In a classical simulation there is no quantum entanglement occurring in the CPU, whereas when we realize the protocol on a QPU there is entanglement and quantum teleportation actually occurs as a physical event. To the extent that the ER=EPR hypothesis then applies, the traversable wormhole dynamics are an equivalent description of this physical event.
Q: If we did not rip a hole in actual spacetime, how can it be that the traversable wormhole dynamics are features of an actual physical event?
A: Maldacena, Stanford, and Yang showed in 2017 that it should be possible using two entangled copies of the SYK model to exhibit the dynamics of a traversable wormhole in a nearly AdS2 spacetime. The dynamics of SYK has no dependence on spatial coordinates, whereas AdS2 has a spatial dimension that provides the traversable path of the wormhole. In analogy with condensed matter physics, one can say that the spatial dimension is “emergent” from the quantum dynamics. This should also apply for our experiment, with the caveats that we used a sparsified version of the SYK model, a somewhat different regime of model parameters, and were not able to write the explicit gravitational dual of the quantum system. While AdS2 is relevant to the emergent “bulk” description, for our small N model we don’t know all the small-N corrections.
Q: Is it not surprising that the Hamiltonian used has commuting terms?
A: The single-sided system has commuting terms due to the optimization for a very simple reduced model. Our fully coupled wormhole Hamiltonian shows operator growth, because the left and right systems do not commute with the interaction.
Q: You claim that the system thermalizes but the commuting Hamiltonian has recurrences: what exactly do you mean by “thermalization”?
A: The relevant time scale for gravitational dynamics is defined by the teleportation time. We observe the decay of two-point functions similarly to a system thermalizing on this time scale. Please watch min 39 of this Dec 4 Princeton seminar by D Jafferis for detail thttps://www.kaltura.com/index.php/extwidget/preview/partner_id/1449362/uiconf_id/14292362/entry_id/1_dfq62s5x/embed/dynamic
Q: What is the new thing we learned about quantum gravity in this study?
A: we learned that the size winding conjecture — which the Stanford group proposed only from the one example of the SYK model — may be correct also in the small-N limit, since it emerged in our learned Hamiltonian “naturally”, i.e. we did not impose it in the machine learning toolbox we used to sparsity the 210 terms N=10 Hamiltonian.
Q: Do our results have any relevance then to the possibility of performing other useful quantum gravity experiments?
A: Yes. Our results support the idea that it is possible to probe traversable wormhole dynamics using relatively small quantum systems realizable on quantum processors. In our case the system was sufficiently small that it could be fully simulated classically as well, but was too coarse-grained for us to probe detailed questions. Now imagine scaling up to ~100 qubit versions: such systems cannot be simulated on classical computers, and one anticipates a bulk description sufficiently fine-grained that one can to probe in some detail features of the emergent wormhole interior.
Acknowledgments
The experiment was performed in collaboration with the Google Quantum AI hardware team, under the direction of A. Megrant, J. Kelly and Y. Chen. We acknowledge the work of the team in fabricating and packaging the processor; building and outfitting the cryogenic and control systems; executing baseline calibrations; optimizing processor performance; and providing the tools to execute the experiment. Specialized device calibration methods were developed bythe physics team led by V. Smelyanskiy. We in particular thank X. Mi and P. Roushan for their technical support in carrying out the experiment and are grateful to B. Kobrin for useful discussions and validation studies. This work is supported by the Department of Energy Office of High Energy Physics QuantISED program grant SC0019219 on Quantum Communication Channels for Fundamental Physics. Additionally, A.Z. acknowledges support from the Hertz Foundation, the Department of Defense through the National Defense Science and Engineering Graduate Fellowship Program, and Caltech’s Intelligent Quantum Networks and Technologies (INQNET) research program. S.I.D is partially supported by the Brinson Foundation. Fermilab is operated by Fermi Research Alliance, LLC under contract number DEAC02- 07CH11359 with the United States Department of Energy. We are grateful to A. Kitaev, J. Preskill, L. Susskind, P. Hayden, A. Brown, S. Nezami, J. Maldacena, N. Yao, K. Thorne and D. Gross for insightful discussions and comments that helped us improve the manuscript. We are also grateful to graduate student O. Cerri for the error analysis of the experimental data. M.S. thanks the members of the QCCFP QuantISED Consortium and acknowledges P. Dieterle for the thorough inspection of the manuscript.
The graphics/artistic representation of the traversable wormhole was done by graduate student A. Mueller.
A quote to love (from this PRL paper in 1988!)
“One can imagine an advanced civilization pulling a wormhole out of the quantum foam and enlarging it to classical size. This might be analyzed by techniques now being developed for computation of spontaneous wormhole production by quantum tunneling.”
The ‘Worms’ QCCFP Team
