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Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials

Author

Listed:
  • Zlatko K. Minev

    (Yorktown Heights
    Mountain View)

  • Khadijeh Najafi

    (Yorktown Heights
    MIT-IBM Watson AI Lab)

  • Swarnadeep Majumder

    (Yorktown Heights)

  • Juven Wang

    (Harvard University
    Royal Institution)

  • Ady Stern

    (Weizmann Institute of Science)

  • Eun-Ah Kim

    (Cornell University
    Ewha Womans University)

  • Chao-Ming Jian

    (Cornell University)

  • Guanyu Zhu

    (Yorktown Heights)

Abstract

The remarkable complexity of a topologically ordered many-body quantum system is encoded in the characteristics of its anyons. Quintessential predictions emanating from this complexity employ the Fibonacci string net condensate (Fib SNC) and its anyons: sampling Fib-SNC would estimate chromatic polynomials while exchanging its anyons would implement universal quantum computation. However, physical realizations remained elusive. We introduce a scalable dynamical string net preparation (DSNP) that constructs Fib SNC and its anyons on reconfigurable graphs suitable for near-term superconducting processors. Coupling the DSNP approach with composite error-mitigation on deep circuits, we create, measure, and braids Fibonacci anyons; charge measurements show 94% accuracy, and exchanging the anyons yields the expected golden ratio ϕ with 98% average accuracy. We then sample the Fib SNC to estimate chromatic polynomial at ϕ + 2 for several graphs. Our results establish the proof of principle for using Fib-SNC and its anyons for fault-tolerant universal quantum computation and aim at a classically hard problem.

Suggested Citation

  • Zlatko K. Minev & Khadijeh Najafi & Swarnadeep Majumder & Juven Wang & Ady Stern & Eun-Ah Kim & Chao-Ming Jian & Guanyu Zhu, 2025. "Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials," Nature Communications, Nature, vol. 16(1), pages 1-9, December.
    • Handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-61493-8
    DOI: 10.1038/s41467-025-61493-8
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    1. Mohsin Iqbal & Nathanan Tantivasadakarn & Ruben Verresen & Sara L. Campbell & Joan M. Dreiling & Caroline Figgatt & John P. Gaebler & Jacob Johansen & Michael Mills & Steven A. Moses & Juan M. Pino & , 2024. "Non-Abelian topological order and anyons on a trapped-ion processor," Nature, Nature, vol. 626(7999), pages 505-511, February.
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