Enhanced fault-tolerant quantum computing in $d$-level systems

Abstract

Error correcting codes protect quantum information and form the basis of fault tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transverse non-Clifford gate. Codes with the desired property are presented for $d$-level, qudit, systems with prime $d$. The codes use $n=d-1$ qudits and can detect upto $\sim d/3$ errors. We quantify the performance of these codes for one approach to quantum computation, known as magic state distillation. Unlike prior work, we find performance is always enhanced by increasing $d$.

Author's final copy. Changes includes correction to plot in figure 1

References in corpus (13)

• Surface codes: Towards practical large-scale quantum computation
• Fault-tolerant quantum computation with high threshold in two dimensions
• Contextuality supplies the magic for quantum computation
• Restrictions on Transversal Encoded Quantum Gate Sets
• Magic state distillation with low overhead
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• Improved magic states distillation for quantum universality
• Multilevel distillation of magic states for quantum computing
• Qudit versions of the qubit "pi-over-eight" gate
• Efficient Decoders for Qudit Topological Codes
• Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function
• Order 3 Symmetry in the Clifford Hierarchy

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