A Universal Circuit Set Using the Quantum Double
arXiv:2411.09697 · doi:10.1038/s41534-025-01063-4
Abstract
One potential route toward fault-tolerant universal quantum computation is to use non-Abelian topological codes. In this work, we investigate how to achieve this goal with the quantum double model -- a specific non-Abelian topological code. By embedding each on-site Hilbert space into a qubit-qutrit pair, we give an explicit construction of the circuits for creating, moving, and locally measuring all non-trivial anyons. We also design a specialized anyon interferometer to remotely measure the total charge of well-separated anyons; this avoids fusion, which would compromise fault tolerance. These protocols enable the implementation of a universal gate set proposed by Cui et al. and active quantum error correction of the circuit-level noise during the computation process. To further reduce the error rate and facilitate error correction, we encode each physical degree of freedom of into a novel, quantum, error-correcting code, enabling fault-tolerant realization, at the logical level, of all gates in the anyon manipulation circuits. Our proposal offers a promising path to realize robust universal topological quantum computation in the NISQ era.
18 pages, 5 figures + 14-page appendix, 1 figure. v2: Added comments on advantages and corrected minor typos. v3: Revised the Summary and Discussion section; added a new section on experimental feasibility
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