4.6 Article

Magic-state distillation with low overhead

期刊

PHYSICAL REVIEW A
卷 86, 期 5, 页码 -

出版社

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.86.052329

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资金

  1. Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontier Center
  2. Korea Foundation for Advanced Studies
  3. DARPA QUEST program [HR0011-09-C-0047]
  4. Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior National Business Center [D11PC20167]
  5. Direct For Mathematical & Physical Scien
  6. Division Of Physics [0803371] Funding Source: National Science Foundation

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We propose a family of error-detecting stabilizer codes with an encoding rate of 1/3 that permit a transversal implementation of the gate T = exp (-i pi Z/8) on all logical qubits. These codes are used to construct protocols for distilling high-quality magic states T |+> by Clifford group gates and Pauli measurements. The distillation overhead scales asO(log(gamma) (1/epsilon)), where epsilon is the output accuracy and gamma = log(2) (3) approximate to 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 twofold overhead reduction for distilling magic states with accuracy epsilon similar to 10(-12) compared with previously known protocols.

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