2012/09/11 by Sergey Bravyi, Jeongwan Haah · 3 citations
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physreva.86.052329
published as Phys. Rev. A 86, 052329 (2012) · 11 pages, 3 figures
arxiv created 2012/09/11 · arxiv updated 2012/11/30
We propose a new family of error detecting stabilizer codes with an encoding rate 1/3 that permit a transversal implementation of the pi/8-rotation T on all logical qubits. The new codes are used to construct protocols for distilling high-quality `magic' states T|+> by Clifford group gates and Pauli measurements. The distillation overhead has a poly-logarithmic scaling as a function of the output accuracy, where the degree of the polynomial is log23≈ 1.6. To construct the desired family of codes, we introduce the notion of a triorthogonal matrix --- a binary matrix in which any pair and any triple of rows have even overlap. Any triorthogonal matrix gives rise to a stabilizer code with a transversal T-gate on all logical qubits, possibly augmented by Clifford gates. A powerful numerical method for generating triorthogonal matrices is proposed. Our techniques lead to a two-fold overhead reduction for distilling magic states with output accuracy 10-12 compared with the best previously known protocol.