Universal quantum computation in the surface code using non-Abelian islands

Abstract

The surface code is currently the primary proposed method for performing quantum error correction. However, despite its many advantages, it has no native method to fault-tolerantly apply non-Clifford gates. Additional techniques are therefore required to achieve universal quantum computation. Here we propose a hybrid scheme which uses small islands of a qudit variant of the surface code to enhance the computational power of the standard surface code. This allows the non-trivial action of the non-Abelian anyons in the former to process information stored in the latter. Specifically, we show that a non-stabilizer state can be prepared, which allows universality to be achieved.

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• Demonstration of weight-four parity measurements in the surface code architecture
• Poking holes and cutting corners to achieve Clifford gates with the surface code
• Simulations of quantum double models
• Improved HDRG decoders for qudit and non-Abelian quantum error correction
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• Non-abelian statistics from an abelian model
• Topological Quantum Computation with Gapped Boundaries

Cited by in corpus (9)

• Anyon condensation and the color code
• Computing data for Levin-Wen with defects
• Bulk-to-boundary anyon fusion from microscopic models
• Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation
• Low-overhead non-Clifford fault-tolerant circuits for all non-chiral abelian topological phases
• Characterization of errors in a CNOT between surface code patches
• Lattice surgery-based logical state teleportation via noisy links
• Defects in Kitaev models and bicomodule algebras
• Universal fault tolerant quantum computation in 2D without getting tied in knots