Magic state distillation with low overhead

Understand

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 $\log_2{3}\approx 1.6$.
• 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.