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

Yi-Cong Zheng*, Ching-Yi Lai, Todd A. Brun, Leong-Chuan Kwek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Fault-tolerant quantum computation (FTQC) schemes using large block codes that encodek> 1 qubits innphysical 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 longin situcomputation 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 inO(1) stepsin situvia either Knill or Steane syndrome measurement circuit, with the qualified ancilla states efficiently prepared. Particularly, for those codes satisfyingk/n similar to 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 distanced. 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.

Original languageEnglish
Article number045007
Number of pages19
JournalQuantum Science and Technology
Issue number4
StatePublished - Oct 2020


  • fault-tolerant quantum computation
  • large block codes
  • quantum error correction
  • Clifford circuit

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