Topological qubits from valence bond solids

Abstract

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 $\frac{2\pi }{N}$, 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.

References in corpus (14)

• Non-Abelian Anyons and Topological Quantum Computation
• Restrictions on Transversal Encoded Quantum Gate Sets
• Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
• Codeword Stabilized Quantum Codes
• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Quantum computational capability of a 2D valence bond solid phase
• On topological phases of spin chains
• Z_3 symmetry-protected topological phases in the SU(3) AKLT model
• Entanglement in an SU(n) Valence-Bond-Solid State
• A simple family of nonadditive quantum codes
• Fault-Tolerant Quantum Error Correction for non-Abelian Anyons
• Qudit quantum computation on matrix product states with global symmetry
• Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models
• Quantum dimer model with Z_2 liquid ground-state: interpolation between cylinder and disk topologies and toy model for a topological quantum-bit

Cited by in corpus (10)

• Approximate symmetries and quantum error correction
• A comparative study of universal quantum computing models: towards a physical unification
• Quasi-exact quantum computation
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
• Nearly degenerate ground states of a checkerboard antiferromagnet and their bosonic interpretation
• Quantum error correction meets continuous symmetries: fundamental trade-offs and case studies
• Response to defects in multi- and bipartite entanglement of isotropic quantum spin networks
• Effect of quantum error correction on detection-induced coherent errors
• Quantum Computing with sine-Gordon Qubits