Quantum Circuits for Measuring Levin-Wen Operators
arXiv:1206.6048 · doi:10.1103/PhysRevB.86.165113
Abstract
We construct quantum circuits for measuring the commuting set of vertex and plaquette operators that appear in the Levin-Wen model for doubled Fibonacci anyons. Such measurements can be viewed as syndrome measurements for the quantum error-correcting code defined by the ground states of this model (the Fibonacci code). We quantify the complexity of these circuits with gate counts using different universal gate sets and find these measurements become significantly easier to perform if n-qubit Toffoli gates with n = 3,4 and 5 can be carried out directly. In addition to measurement circuits, we construct simplified quantum circuits requiring only a few qubits that can be used to verify that certain self-consistency conditions, including the pentagon equation, are satisfied by the Fibonacci code.
12 pages, 13 figures; published version
References in corpus (10)
- Fault-tolerant quantum computation with high threshold in two dimensions
- Topological Quantum Distillation
- Topological fault-tolerance in cluster state quantum computation
- Quantum computing with nearest neighbor interactions and error rates over 1%
- Realization of the quantum Toffoli gate with trapped ions
- Efficient Toffoli Gates Using Qudits
- Topological Computation without Braiding
- Topological Quantum Compiling
- Exact entanglement renormalization for string-net models
- Space-Time Geometry of Topological phases