Magic state distillation in all prime dimensions using quantum Reed-Muller codes

Abstract

We propose families of protocols for magic state distillation -- important components of fault tolerance schemes --- for systems of odd prime dimension. Our protocols utilize quantum Reed-Muller codes with transversal non-Clifford gates. We find that, in higher dimensions, small and effective codes can be used that have no direct analogue in qubit (two-dimensional) systems. We present several concrete protocols, including schemes for three-dimensional (qutrit) and five-dimensional (ququint) systems. The five-dimensional protocol is, by many measures, the best magic state distillation scheme yet discovered. It excels both in terms of error threshold with respect to depolarising noise (36.3%) and the efficiency measure know as "yield", where, for a large region of parameters, it outperforms its qubit counterpart by many orders of magnitude.

Updated from V1 to include results on the remarkable d=5 case

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Cited by in corpus (12)

• Electromagnetic Force and Momentum
• Electromagnetic Angular Momentum
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Multilevel distillation of magic states for quantum computing
• A magic state's fidelity can be superior to the operations that created it
• Distilling one-qubit magic states into Toffoli states
• Error Thresholds for Abelian Quantum Double Models: Increasing the bit-flip Stability of Topological Quantum Memory
• Improved HDRG decoders for qudit and non-Abelian quantum error correction
• Maximum nonlocality and minimum uncertainty using magic states
• Quantum Information Processing by Weaving Quantum Talbot Carpets
• Order 3 Symmetry in the Clifford Hierarchy
• Measurement-only topological quantum computation without forced measurements