Constant depth fault-tolerant Clifford circuits for multi-qubit large block codes

• URL: http://arxiv.org/abs/2003.12328v2
• Date: Sat, 1 Aug 2020 13:43:25 GMT
• Title: Constant depth fault-tolerant Clifford circuits for multi-qubit large block codes
• Authors: Yi-Cong Zheng, Ching-Yi Lai, Todd A. Brun, Leong-Chuan Kwek
• Abstract summary: This paper focuses on Calderbank-Shor-Steane $[![ n,k,d ]!]$ (CSS) codes and their logical FT Clifford circuits. We show that the depth of an arbitrary logical Clifford circuit can be implemented fault-tolerantly in $O(1)$ steps emphin-situ via either Knill or Steane syndrome measurement circuit.
• Score: 2.3513645401551333
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fault-tolerant quantum computation (FTQC) schemes using large block codes that encode $k>1$ qubits in $n$ physical qubits can potentially reduce the resource overhead to a great extent because of their high encoding rate. However, the fault-tolerant (FT) logical operations for the encoded qubits are difficult to find and implement, which usually takes not only a very large resource overhead but also long $\textit{in-situ}$ computation time. In this paper, we focus on Calderbank-Shor-Steane $[\![ n,k,d ]\!]$ (CSS) codes and their logical FT Clifford circuits. We show that the depth of an arbitrary logical Clifford circuit can be implemented fault-tolerantly in $O(1)$ steps \emph{in-situ} via either Knill or Steane syndrome measurement circuit, with the qualified ancilla states efficiently prepared. Particularly, for those codes satisfying $k/n\sim \Theta(1)$, the resource scaling for Clifford circuits implementation on the logical level can be the same as on the physical level up to a constant, which is independent of code distance $d$. With a suitable pipeline to produce ancilla states, our scheme requires only a modest resource cost in physical qubits, physical gates, and computation time for very large scale FTQC.

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