Coherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and are more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with constant-excitation codes by code concatenation. Namely, by concatenating an [[n, k, d]] stabilizer outer code with dual-rail inner codes, we obtain a [[2n, k, d]] constant-excitation code immune from coherent phase errors and also equivalent to a Pauli-rotated stabilizer code. When the stabilizer outer code is fault-tolerant, the constant-excitation code has a positive fault-tolerant threshold against stochastic errors. Setting the outer code as a four-qubit amplitude damping code yields an eight-qubit constant-excitation code that corrects a single amplitude damping error, and we analyze this code’s potential as a quantum memory.

由集体耦合引起的相干误差是许多现实量子系统中的主要噪声形式，并且比通常认为的随机误差更具破坏性。在这里，我们建议通过代码串联将稳定器代码与恒定激励代码相结合。即，通过将 [[ n ,  k ,  d ]] 稳定器外码与双轨内码连接起来，我们得到 [[2 n ,  k ,  d]] 不受相干相位误差影响的恒定激励代码，也相当于泡利旋转稳定器代码。当稳定器外码具有容错能力时，恒激励码对随机误差具有正容错阈值。将外部代码设置为四量子位振幅阻尼代码会产生一个八量子位恒定激励代码，该代码可纠正单个振幅阻尼误差，我们分析了该代码作为量子存储器的潜力。