  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.
