Quantum hashing with the icosahedral group
arXiv:0903.1497 · doi:10.1103/PhysRevLett.104.160502
Abstract
We study an efficient algorithm to hash any single qubit gate (or unitary matrix) into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudo-groups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O[log(1/epsilon)], we can approximate all SU(2) matrices to an average error epsilon with a cost of O[log(1/epsilon)] in time. The algorithm is applicable to generic quantum compiling.
5 pages, 4 figures; revised version, to appear in Phys. Rev. Lett.
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- Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate
- Genetic braid optimization: A heuristic approach to compute quasiparticle braids
- Topological Quantum Gate Construction by Iterative Pseudogroup Hashing
- Topological Insulating Phases of Non-Abelian Anyonic Chains
- Topological quantum compilation of metaplectic anyons based on the genetic optimized algorithms
- Topological quantum compilation of two-qubit gates
- Weighted Quantum Channel Compiling through Proximal Policy Optimization
- Genetic algorithm enhanced Solovay-Kitaev algorithm for quantum compiling of Fibonacci anyons
- The construction of a universal quantum gate set for the SU(2)k (k=5,6,7) anyon models via genetic optimized algorithm
- Platonic Bell inequalities for all dimensions