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We developed a new algorithm to represent quantum operations using Fibonacci anyon braids. This significantly reduces the depth of quantum computations, improving efficiency for braiding and quantum gate approximations.

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Area of Science:

  • Quantum computation
  • Topological quantum computation
  • Condensed matter physics

Background:

  • Non-Abelian anyons and the Fibonacci model are key to topological quantum computation.
  • Compiling quantum operations into braiding is crucial for fault-tolerant quantum computers.

Purpose of the Study:

  • To develop an efficient method for compiling quantum operations into braid representations.
  • To approximate single-qubit and two-qubit gates using Fibonacci anyon braids.
  • To achieve depth-optimal braid patterns for quantum computations.

Main Methods:

  • Classification of single-qubit unitaries representable by Fibonacci anyon braids.
  • Development of a probabilistically polynomial time algorithm for approximating quantum gates.
  • Extension of the algorithm to generate weaves and approximate two-qubit gates.

Main Results:

  • Identified exact representations for single-qubit unitaries using Fibonacci anyon braids.
  • Created an algorithm that approximates any single-qubit unitary with desired precision.
  • Achieved braid pattern depths 20 to 1000 times shorter than previous methods.

Conclusions:

  • The developed algorithm offers significant depth reduction for compiled quantum operations.
  • The method provides efficient approximations for both single- and two-qubit gates.
  • This work advances the practical implementation of topological quantum computation using anyons.