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

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Computational Complexity

Background:

• Topologically ordered many-body quantum systems possess complexity encoded in their anyons.
• Fibonacci string net condensates (Fib SNC) and their anyons are predicted to enable universal quantum computation and chromatic polynomial estimation.
• Physical realization of these systems has been a significant challenge.

Purpose of the Study:

• To introduce a scalable method for preparing Fibonacci string net condensates and their anyons.
• To demonstrate the creation, measurement, and braiding of Fibonacci anyons on near-term superconducting processors.
• To establish a proof of principle for fault-tolerant quantum computation and classically hard problem-solving using Fib SNC.

Main Methods:

• Development of a scalable dynamical string net preparation (DSNP) for constructing Fib SNC on reconfigurable graphs.
• Implementation of composite error-mitigation techniques on deep quantum circuits.
• Experimental creation, measurement, and braiding of Fibonacci anyons using superconducting qubits.

Main Results:

• Successful construction and manipulation of Fibonacci anyons with high accuracy (94% for charge measurements).
• Experimental verification of braiding operations, yielding the golden ratio (ϕ) with 98% average accuracy.
• Demonstration of sampling Fib SNC to estimate chromatic polynomials for various graphs.

Conclusions:

• The DSNP approach provides a viable pathway for realizing topological quantum computation.
• This work establishes the foundation for using Fib SNC and anyons for fault-tolerant quantum computation.
• The developed methods offer a potential solution for tackling classically hard computational problems.