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

Abstract

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
Volume5
Issue number4
DOIs
StatePublished - Oct 2020

Keywords

  • fault-tolerant quantum computation
  • large block codes
  • quantum error correction
  • Clifford circuit
  • ERROR-CORRECTING CODES
  • QUANTUM COMPUTATION
  • ACCURACY THRESHOLD

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