Authors:

Rafael Casas Lozano

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About Paper:

The pursuit of constructing a fault-tolerant quantum computer is becoming increasingly feasible due to advancements in topological quantum computing. This approach employs quasi-particles in two dimensions, known as anyons, which exist in topological phases of matter. The braiding of anyons induces unitary transformations that function as quantum logic gates, achieving hardware-level fault tolerance. Unlike the standard circuit model, the multi-anyon spaces in topological quantum computing seldom have an exact tensor product structure. Hence, a crucial problem is determining if there exist braiding gates that are leakage-free and entangling. We focus on two important anyon systems, the Fibonacci anyon and the anyons of the double group of the permutation group \( S_3 \) (denoted as \( D(S_3) \)). It is conjectured that leakage-free entangling gates do not exist in the Fibonacci anyon system, while such gates do exist in the \( D(S_3) \) system. This study aims to determine whether it is possible to find or approximate leakage-free entangling quantum gates in anyonic systems. The initial phase involves calculating the basic braidings \( \sigma_1 \) through \( \sigma_5 \) for a 6-anyon Fibonacci system and representing them with F-matrices and R-symbols. Subsequently, various combinations will be tested to identify leakage-free entangling gates, a process repeated for the \( D(S_3) \) anyon system. The study will either confirm the existence of leakage-free entangling gates in these anyon systems or provide numerical and theoretical evidence for their non-existence. These results will enhance our understanding of the entangling capabilities of anyonic systems and suggest new research directions with potential practical implications for the development of robust quantum computing technologies. Keywords: [no keywords provided]

Source:

Purdue University / 2024

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Co-authors:

Rafael Casas Lozano