Magic state distillation with low overhead

Abstract

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.

11 pages, 3 figures

References in corpus (4)

• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological fault-tolerance in cluster state quantum computation
• Restrictions on Transversal Encoded Quantum Gate Sets
• Improved magic states distillation for quantum universality

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• Distilling one-qubit magic states into Toffoli states
• Reducing the quantum computing overhead with complex gate distillation
• A Non-Commuting Stabilizer Formalism
• Quantum circuit optimization by topological compaction in the surface code
• Magic State Distillation and Gate Compilation in Quantum Algorithms for Quantum Chemistry
• Hybrid magic state distillation for universal fault-tolerant quantum computation
• Resource optimization for fault-tolerant quantum computing
• Resource comparison of two surface code implementations of small angle Z rotations