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Register a new userClasses of topological qubits from low-dimensional quantum spin systems
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Authors
Dong-Sheng Wang
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Topological phases of matter is a natural place for encoding robust qubits for quantum computation. In this work we extend the newly introduced class of qubits based on valence-bond solid models with SPT (symmetry-protected topological) order to more general cases. Furthermore, we define and compare various classes of topological qubits encoded in the bulk ground states of topological systems, including SSB (spontaneous symmetry-breaking), TOP (topological), SET (symmetry-enriched topological), SPT, and subsystem SPT classes. We focus on several features for qubits to be robust, including error sets, logical support, code distance and shape of logical gates. In particular, when a global U(1) symmetry is present and preserved, we find a twist operator that extracts the SPT order plays the role of a topological logical operator, which is suitable for global implementation.
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Topological qubits based on $SU(N)$-symmetric valence-bond solid models are constructed. A logical topological qubit is the ground subspace with two-fold degeneracy, which is due to the spontaneous breaking of a global parity symmetry. A logical $Z$-rotation by angle $frac{2pi}{N}$, for any integer $N > 2$, is provided by a global twist operation, which is of topological nature and protected by the energy gap. A general concatenation scheme with standard quantum error-correction codes is also proposed, which can lead to better codes. Generic error-correction properties of symmetry-protected topological order are also demonstrated.
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