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<p>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 <i>ϕ</i> with 98% average accuracy. We then sample the Fib SNC to estimate chromatic polynomial at <i>ϕ</i>&#xa0;+&#xa0;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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月6日

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  • Zlatko K. Minev,
  • Khadijeh Najafi,
  • Swarnadeep Majumder,
  • Juven Wang,
  • Ady Stern,
  • Eun-Ah Kim,
  • Chao-Ming Jian,
  • Guanyu Zhu

摘要

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.