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

Zlatko K. Minev, Khadijeh Najafi, Swarnadeep Majumder, Juven Wang, Ady Stern, Eun-Ah Kim (), Chao-Ming Jian () and Guanyu Zhu
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Zlatko K. Minev: Yorktown Heights
Khadijeh Najafi: Yorktown Heights
Swarnadeep Majumder: Yorktown Heights
Juven Wang: Harvard University
Ady Stern: Weizmann Institute of Science
Eun-Ah Kim: Cornell University
Chao-Ming Jian: Cornell University
Guanyu Zhu: Yorktown Heights

Nature Communications, 2025, vol. 16, issue 1, 1-9

Abstract: 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.

Date: 2025
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DOI: 10.1038/s41467-025-61493-8

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