Magic-state distillation with low overhead

By Sergey Bravyi, Jeongwan Haah. 2012

441 citations recorded by the source corpus.

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. 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.

View Paper: https://www.semanticscholar.org/paper/76b653734f963725247de00b2eab822f967bb3e5

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Citations in the corpus

A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery (2018, methodology): “Here, we discuss a general procedure that can be applied to any distillation protocol based on an errorcorrecting code with transversal T gates, such as punctured Reed-Muller codes [16, 17] or block codes [18–20].”
The resource theory of stabilizer quantum computation (2013, methodology): “Efficiency of the [[5, 1, 3]]3 qutrit code of [1].”
Magic State Distillation: Not as Costly as You Think (2019, methodology): “d in the previous sections can be used to implement any distillation protocol that can be expressed as a sequence of Z-type π/8 rotations, e.g., all protocols that are based on triorthogonal matrices [8,16]. A very similar class of protocols are synthillation protocols, whose implementation we discu”