Constant depth fault-tolerant Clifford circuits for multi-qubit large block codes
Yi-Cong Zheng, Ching-Yi Lai, Todd A Brun, Leong-Chuan Kwek · Quantum Science and Technology · 2020
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 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 in situ via either Knill or Steane syndrome measurement circuit, with the qualified ancilla states efficiently prepared. Particularly, for those codes satisfying k / n ∼ Θ(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.