Magic-state distillation with low overhead

作者：Bravyi Sergey^*; Haah Jeongwan

来源：Physical Review A, 2012, 86(5): 052329.

DOI：10.1103/PhysRevA.86.052329

We propose a family of error-detecting stabilizer codes with an encoding rate of 1/3 that permit a transversal implementation of the gate T = exp (-i pi Z/8) on all logical qubits. These codes are used to construct protocols for distilling high-quality "magic" states T |+> by Clifford group gates and Pauli measurements. The distillation overhead scales asO(log(gamma) (1/epsilon)), where epsilon is the output accuracy and gamma = log(2) (3) approximate to 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 twofold overhead reduction for distilling magic states with accuracy epsilon similar to 10(-12) compared with previously known protocols.

• 出版日期2012-11-27