Traversable wormhole dynamics on a quantum processor

Traversable wormhole dynamics on a quantum processor

Play all audios:

Loading...

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. Access through your institution Buy or subscribe This is a preview of subscription


content, access via your institution ACCESS OPTIONS Access through your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access


subscription $32.99 / 30 days cancel any time Learn more Subscribe to this journal Receive 51 print issues and online access $199.00 per year only $3.90 per issue Learn more Buy this article


* Purchase on SpringerLink * Instant access to full article PDF Buy now Prices may be subject to local taxes which are calculated during checkout ADDITIONAL ACCESS OPTIONS: * Log in * Learn


about institutional subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS A QUANTUM PROCESSOR BASED ON COHERENT TRANSPORT OF ENTANGLED ATOM ARRAYS


Article Open access 20 April 2022 MEASUREMENT-INDUCED ENTANGLEMENT AND TELEPORTATION ON A NOISY QUANTUM PROCESSOR Article Open access 18 October 2023 PROBING ENTANGLEMENT IN A 2D HARD-CORE


BOSE–HUBBARD LATTICE Article Open access 24 April 2024 DATA AVAILABILITY Data from this work are available upon request. CODE AVAILABILITY Code from this work is available upon request.


CHANGE HISTORY * _ 04 APRIL 2025 A Correction to this paper has been published: https://doi.org/10.1038/s41586-025-08788-4 _ REFERENCES * Maldacena, J. The large-N limit of superconformal


field theories and supergravity. _Int. J. Theor. Phys._ 38, 1113–1133 (1999). MathSciNet  MATH  Google Scholar  * Sachdev, S. & Ye, J. Gapless spin-fluid ground state in a random quantum


Heisenberg magnet. _Phys. Rev. Lett._ 70, 3339–3342 (1993). ADS  CAS  PubMed  MATH  Google Scholar  * Kitaev, A. A simple model of quantum holography. In _Proc. KITP: Entanglement in


Strongly-Correlated Quantum Matter_ 12 (eds Grover, T. et al.) 26 (Univ. California, Santa Barbara, 2015). * Maldacena, J. & Stanford, D. Remarks on the Sachdev-Ye-Kitaev model. _Phys.


Rev. D_ 94, 106002 (2016). ADS  MathSciNet  MATH  Google Scholar  * Almheiri, A. & Polchinski, J. Models of AdS2 backreaction and holography. _J. High Energy Phys._ 11, 014 (2015). ADS 


MATH  Google Scholar  * Gross, D. J. & Rosenhaus, V. The bulk dual of SYK: cubic couplings. _J. High Energy Phys._ 05, 092 (2017). ADS  MathSciNet  MATH  Google Scholar  * Maldacena, J.


& Susskind, L. Cool horizons for entangled black holes. _Fortschr. Phys._ 61, 781–811 (2013). MathSciNet  MATH  Google Scholar  * Susskind, L. Dear qubitzers, GR=QM. Preprint at


https://doi.org/10.48550/arXiv.1708.03040 (2017). * Gao, P. & Jafferis, D. L. A traversable wormhole teleportation protocol in the SYK model. _J. High Energy Phys._ 2021, 97 (2021). *


Maldacena, J., Stanford, D. & Yang, Z. Diving into traversable wormholes. _Fortschr. Phys._ 65, 1700034 (2017). MathSciNet  MATH  Google Scholar  * Brown, A. R. et al. Quantum gravity in


the lab: teleportation by size and traversable wormholes. Preprint at https://doi.org/10.48550/arXiv.1911.06314 (2021). * Nezami, S. et al. Quantum gravity in the lab: teleportation by size


and traversable wormholes, part II. Preprint at https://doi.org/10.48550/arXiv.2102.01064 (2021). * Schuster, T. et al. Many-body quantum teleportation via operator spreading in the


traversable wormhole protocol. _Phys. Rev. X_ 12, 031013 (2022). * Gao, P., Jafferis, D. L. & Wall, A. C. Traversable wormholes via a double trace deformation. _J. High Energy Phys._


2017, 151 (2017). ADS  MathSciNet  MATH  Google Scholar  * Maldacena, J. & Qi, X.-L. Eternal traversable wormhole. Preprint at https://doi.org/10.48550/arXiv.1804.00491 (2018). * Cotler,


J. S. et al. Black holes and random matrices. _J. High Energy Phys._ 2017, 118 (2017). MathSciNet  MATH  Google Scholar  * Kitaev, A. & Suh, S. J. The soft mode in the Sachdev-Ye-Kitaev


model and its gravity dual. _J. High Energy Phys._ 2018, 183 (2018). MathSciNet  MATH  Google Scholar  * Berkooz, M., Narayan, P., Rozali, M. & Simón, J. Higher dimensional


generalizations of the SYK model. _J. High Energy Phys._ 01, 138 (2017). ADS  MathSciNet  MATH  Google Scholar  * Witten, E. An SYK-like model without disorder. _J. Phys. A._ 52, 474002


(2019). ADS  MathSciNet  CAS  MATH  Google Scholar  * Witten, E. Anti-de Sitter space and holography. _Adv. Theor. Math. Phys._ 2, 253–291 (1998). ADS  MathSciNet  MATH  Google Scholar  *


Gubser, S., Klebanov, I. & Polyakov, A. Gauge theory correlators from non-critical string theory. _Phys. Lett. B._ 428, 105–114 (1998). ADS  MathSciNet  CAS  MATH  Google Scholar  *


Hochberg, D. & Visser, M. The null energy condition in dynamic wormholes. _Phys. Rev. Lett._ 81, 746–749 (1998). ADS  MathSciNet  CAS  MATH  Google Scholar  * Morris, M. S., Thorne, K.


S. & Yurtsever, U. Wormholes, time machines, and the weak energy condition. _Phys. Rev. Lett._ 61, 1446–1449 (1988). ADS  CAS  PubMed  MATH  Google Scholar  * Visser, M., Kar, S. &


Dadhich, N. Traversable wormholes with arbitrarily small energy condition violations. _Phys. Rev. Lett._ 90, 201102 (2003). ADS  MathSciNet  PubMed  MATH  Google Scholar  * Visser, M.


_Lorentzian Wormholes: From Einstein to Hawking. Computational and Mathematical Physics_ (American Institute of Physics, 1995). * Graham, N. & Olum, K. D. Achronal averaged null energy


condition. _Phys. Rev. D_ 76, 064001 (2007). ADS  MATH  Google Scholar  * Arute, F. et al. Quantum supremacy using a programmable superconducting processor. _Nature_ 574, 505–510 (2019). ADS


  CAS  PubMed  MATH  Google Scholar  * Maldacena, J., Stanford, D. & Yang, Z. Conformal symmetry and its breaking in two dimensional nearly anti-de-Sitter space. _Prog. Theor. Exp.


Phys._ 2016, 12C104 (2016). MATH  Google Scholar  * Maldacena, J. Eternal black holes in anti-de sitter. _J. High Energy Phys._ 2003, 021–021 (2003). MathSciNet  MATH  Google Scholar  *


Hayden, P. & Preskill, J. Black holes as mirrors: quantum information in random subsystems. _J. High Energy Phys._ 2007, 120 (2007). MathSciNet  MATH  Google Scholar  * Susskind, L.


& Zhao, Y. Teleportation through the wormhole. _Phys. Rev. D_ 98, 046016 (2018). ADS  MathSciNet  CAS  MATH  Google Scholar  * Gao, P. & Liu, H. Regenesis and quantum traversable


wormholes. _J. High Energy Phys._ 10, 048 (2019). ADS  MathSciNet  MATH  Google Scholar  * Yoshida, B. & Yao, N. Y. Disentangling scrambling and decoherence via quantum teleportation.


_Phys. Rev. X_ 9, 011006 (2019). CAS  MATH  Google Scholar  * Landsman, K. A. et al. Verified quantum information scrambling. _Nature_ 567, 61–65 (2019). ADS  CAS  PubMed  MATH  Google


Scholar  * Berkooz, M., Isachenkov, M., Narovlansky, V. & Torrents, G. Towards a full solution of the large N double-scaled SYK model. _J. High Energy Phys._ 03, 079 (2019). ADS 


MathSciNet  MATH  Google Scholar  * García-García, A. M. & Verbaarschot, J. J. M. Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model. _Phys. Rev. D_ 94, 126010 (2016).


ADS  MATH  Google Scholar  * García-García, A. M. & Verbaarschot, J. J. M. Analytical spectral density of the Sachdev-Ye-Kitaev model at finite _n_. _Phys. Rev. D_ 96, 066012 (2017). *


Xu, S., Susskind, L., Su, Y. & Swingle, B. A sparse model of quantum holography. Preprint at https://doi.org/10.48550/arXiv.2008.02303 (2020). * Garcia-Garcia, A. M., Jia, Y., Rosa, D.


& Verbaarschot, J. J. M. Sparse Sachdev-Ye-Kitaev model, quantum chaos, and gravity duals. _Phys. Rev. D_ 103, 106002 (2021). ADS  MathSciNet  CAS  MATH  Google Scholar  * Caceres, E.,


Misobuchi, A. & Pimentel, R. Sparse SYK and traversable wormholes. _J. High Energy Phys._ 11, 015 (2021). ADS  MathSciNet  MATH  Google Scholar  * Kandala, A. et al. Hardware-efficient


variational quantum eigensolver for small molecules and quantum magnets. _Nature_ 549, 242–246 (2017). ADS  CAS  PubMed  Google Scholar  * Cottrell, W., Freivogel, B., Hofman, D. M. &


Lokhande, S. F. How to build the thermofield double state. _J. High Energy Phys._ 2019, 58 (2019). MathSciNet  MATH  Google Scholar  * Huggins, W. J. et al. Virtual distillation for quantum


error mitigation. _Phys. Rev. X_ 11, 041036 (2021). CAS  MATH  Google Scholar  * O’Brien, T. E. et al. Error mitigation via verified phase estimation. _PRX Quantum_ 2, 020317 (2021). ADS 


Google Scholar  * Temme, K., Bravyi, S. & Gambetta, J. M. Error mitigation for short-depth quantum circuits. _Phys. Rev. Lett._ 119, 180509 (2017). ADS  MathSciNet  PubMed  MATH  Google


Scholar  * Li, Y. & Benjamin, S. C. Efficient variational quantum simulator incorporating active error minimization. _Phys. Rev. X_ 7, 021050 (2017). Google Scholar  * Kolchmeyer, D. K.


_Toy Models of Quantum Gravity_. PhD thesis, Harvard Univ. (2022); https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37372099. * Zlokapa, A. _Quantum Computing for Machine Learning and Physics


Simulation_. BSc thesis, California Institute of Technology (2021); https://doi.org/10.7907/q75q-zm20. Download references 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. AUTHOR INFORMATION Author notes * These authors contributed equally: Daniel Jafferis, Alexander Zlokapa AUTHORS AND


AFFILIATIONS * Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA, USA Daniel Jafferis & David K. Kolchmeyer * Center for Theoretical Physics, Massachusetts


Institute of Technology, Cambridge, MA, USA Alexander Zlokapa * Division of Physics, Mathematics and Astronomy, Caltech, Pasadena, CA, USA Alexander Zlokapa, Samantha I. Davis, Nikolai Lauk 


& Maria Spiropulu * Alliance for Quantum Technologies (AQT), California Institute of Technology, Pasadena, CA, USA Alexander Zlokapa, Samantha I. Davis, Nikolai Lauk & Maria


Spiropulu * Google Quantum AI, Venice, CA, USA Alexander Zlokapa & Hartmut Neven * Fermilab Quantum Institute and Theoretical Physics Department, Fermi National Accelerator Laboratory,


Batavia, IL, USA Joseph D. Lykken Authors * Daniel Jafferis View author publications You can also search for this author inPubMed Google Scholar * Alexander Zlokapa View author publications


You can also search for this author inPubMed Google Scholar * Joseph D. Lykken View author publications You can also search for this author inPubMed Google Scholar * David K. Kolchmeyer View


author publications You can also search for this author inPubMed Google Scholar * Samantha I. Davis View author publications You can also search for this author inPubMed Google Scholar *


Nikolai Lauk View author publications You can also search for this author inPubMed Google Scholar * Hartmut Neven View author publications You can also search for this author inPubMed Google


Scholar * Maria Spiropulu View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS 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. CORRESPONDING AUTHOR Correspondence to


Maria Spiropulu. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. PEER REVIEW PEER REVIEW INFORMATION _Nature_ thanks the anonymous reviewers for their


contribution to the peer review of this work. ADDITIONAL INFORMATION PUBLISHER’S NOTE Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional


affiliations. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION This file contains Supplementary Sections 1–7 including Figs. 1–36 and References: see the Contents for details. RIGHTS AND


PERMISSIONS Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other


rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Reprints and


permissions ABOUT THIS ARTICLE CITE THIS ARTICLE 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 Download citation * Received: 22 February 2022 * Accepted: 07 October 2022 * Published: 30 November 2022 * Issue Date: 01 December 2022 * DOI:


https://doi.org/10.1038/s41586-022-05424-3 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get shareable link Sorry, a shareable link is not


currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative