Optimize qubit ordering for CAMPS simulation

Develop methods to determine or optimize the qubit ordering used by Clifford-augmented matrix product state (CAMPS) simulation so as to reduce the entanglement of the magic residual and improve simulation performance beyond the current greedy local disentangler.

Background

The CAMPS representation separates a quantum state into a Clifford frame and a magic residual represented as a matrix product state. Although the Clifford frame can absorb qubit permutations through SWAP operations, the state-of-the-art disentangler used in the simulations performs only a greedy local search over nearest-neighbour Clifford gates. Consequently, it may fail to identify the globally optimal qubit ordering or Clifford gauge.

The authors report that their hand-designed qubit layout improves CAMPS runtime relative to random ordering, but they do not establish an optimal ordering procedure. Systematically exploring this dependence could reduce the bond dimension of the magic residual and improve CAMPS performance for cultivation circuits with less obvious structure.

References

Thus, it will not necessarily find the optimal. We found that starting the CAMPS simulation with the qubit layout presented in the previous section reduced the simulation time of CAMPS by $25\%$ on average compared to random ordering, showing significantly less dependence than pure MPS on qubit ordering. All simulations presented below are performed with the same layouts as pure MPS. Further exploration of this dependency is left for future work.

— Comparing magic state cultivation methods using matrix product states  (2609.19116 - Hartweg et al., 16 Sep 2026) in Section 3.2, subsection “Clifford augmented MPS”