Toward constructing a large-scale quantum computer based on TQFT

Topological quantum computation, motivated by topological quantum field theory (TQFT), offers a promising path toward fault-tolerant universal quantum computation. However, the practical realization of such a system remains challenging due to the difficulty of finding suitable topological materials. In this work, we provide a comprehensive blueprint for constructing a fault-tolerant universal quantum computer based on the quantum double model $\mathcal{D}(S_3)$, a specific non-Abelian topological order. We implement logical computations using quantum circuits on qubits and qutrits, including a single non-Clifford gate, compatible with near-term quantum devices. This work bridges the gap between abstract mathematical frameworks and noise-resilient quantum computation on near-term devices. Our proposal offers a promising path to realize a non-Abelian anyon-based large scale quantum computer.

Based on https://arxiv.org/abs/2411.09697

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