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Traversable wormhole dynamics on a quantum processor

Abstract

The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary. The anti-de Sitter (AdS)/conformal field theory correspondence or duality1 is the principal example of holography. The Sachdev–Ye–Kitaev (SYK) model of N 1 Majorana fermions2,3 has features suggesting the existence of a gravitational dual in AdS2, and is a new realization of holography4,5,6. We invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry7,8 through the traversable wormhole mechanism as implemented in the SYK model9,10. A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol9. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits9. Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding11,12,13, coupling on either side of the wormhole that is consistent with a negative energy shockwave14, a Shapiro time delay15, causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics16,17. Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals18 and other SYK-like models19.

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Fig. 1: Traversable wormhole in spacetime and in the holographic dual.
Fig. 2: Learning a traversable wormhole Hamiltonian from the SYK model.
Fig. 3: Signatures of wormhole traversability for the learned Hamiltonian.
Fig. 4: Observation of traversable wormhole dynamics.

Data availability

Data from this work are available upon request.

Code availability

Code from this work is available upon request.

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Acknowledgements

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 by the 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 programme grant no. SC0019219 on Quantum Communication Channels for Fundamental Physics. Furthermore, 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 research programme. S.I.D. is partially supported by the Brinson Foundation. Fermilab is operated by Fermi Research Alliance, LLC under contract number DE-AC02-07CH11359 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 (Quantum Communication Channels for Fundamental Physics) QuantISED Consortium and acknowledges P. Dieterle for the thorough inspection of the manuscript.

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J.D.L. and D.J. are senior co-principal investigators of the QCCFP Consortium. J.D.L. worked on the conception of the research program, theoretical calculations, computation aspects, simulations and validations. D.J. is one of the inventors of the SYK traversable wormhole protocol. He worked on all theoretical aspects of the research and the validation of the wormhole dynamics. Graduate student D.K.K.47 worked on theoretical aspects and calculations of the chord diagrams. Graduate student S.I.D. worked on computation and simulation aspects. Graduate student A.Z.48 worked on all theory and computation aspects, the learning methods that solved the sparsification challenge, the coding of the protocol on the Sycamore and the coordination with the Google Quantum AI team. Postdoctoral scholar N.L. worked on the working group coordination aspects, meetings and workshops, and follow-up on all outstanding challenges. Google’s VP Engineering, Quantum AI, H.N. coordinated project resources on behalf of the Google Quantum AI team. M.S. is the lead principal investigator of the QCCFP Consortium Project. She conceived and proposed the on-chip traversable wormhole research program in 2018, assembled the group with the appropriate areas of expertise and worked on all aspects of the research and the manuscript together with all authors.

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Correspondence to Maria Spiropulu.

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Jafferis, D., Zlokapa, A., Lykken, J.D. et al. Traversable wormhole dynamics on a quantum processor. Nature 612, 51–55 (2022). https://doi.org/10.1038/s41586-022-05424-3

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