This paper introduces SymFT, a new classical simulator for a common class of fault‑tolerant quantum circuits. These circuits are dominated by Clifford operations—gates that keep a simple algebraic structure—but also include a smaller number of non‑Clifford rotations (for example T gates), Pauli measurements, and Pauli‑type noise. SymFT focuses on these “Clifford‑dominated” circuits and reports substantial speedups over recent simulators on the tested examples.

The authors build SymFT from two main ideas. First, they perform a symbolic Clifford–Pauli frame factorization. In plain terms, they push the non‑Clifford rotations and measurements back through the Clifford parts of the circuit so that the remaining operation that sets branch probabilities is a sequence of Pauli rotations and Pauli projectors. Noise and measurement‑dependent feedback are kept as simple symbolic signs. Because the remaining Clifford and Pauli frames are unitary, they do not change the probabilities of measurement outcomes. That means SymFT does not need to reapply those unitary frames for every sample shot, which saves time.

Second, SymFT uses adaptive stabilizer‑coordinate planning. The simulator picks a shared stabilizer basis (a way of describing the easy part of the state) and stores only the active non‑stabilizer degrees of freedom in a compact dense vector whose size grows or shrinks as needed. The planner resolves basis changes once up front and compiles direct sampling instructions that act on that dense active vector. This avoids repeated tableau updates and avoids extra Clifford transformations that other approaches can introduce during sampling.

Why this matters: classical simulation is an important tool for designing and validating fault‑tolerant quantum protocols, including error correction and magic‑state procedures that introduce the needed non‑Clifford operations. By avoiding per‑shot unitary bookkeeping and by concentrating the costly work into a small active vector, SymFT achieves state‑of‑the‑art sampling speed on the circuits the authors tested. On a single CPU core it ran 2.51–2.56 times faster than Stim for surface‑code circuits, and 1.86–3.51 times faster than Clifft on tested magic‑state cultivation and distillation circuits. For cultivation circuits, its throughput exceeded the authors’ earlier simulator SOFT by more than two orders of magnitude. The package is provided as Python code with C++ CPU and CUDA GPU back ends.