Lean-Mechanized QPPM Compiler Cuts Verified Logical Measurement Depth 17.9% on QASMBench

The work defines QPPM as a terminating language whose weakest-precondition semantics, expressed via store-indexed matrix assertions, directly encodes both quantum state and classical outcome constraints required for fault-tolerant gate compilation. Soundness and relative completeness follow immediately from termination, enabling compositional verification of Clifford+T lowering, magic-state injection, outcome hiding, and post-optimization scheduling without separate proof obligations for each transformation.

Prior quantum Hoare logics handled either pure state evolution or classical control separately; the present calculus unifies them so that an optimizer pass can be shown to preserve every externally observable outcome while eliminating redundant measurements. A separate approximation relation then bounds synthesis error propagation to trace distance, allowing the pipeline to select the lowest certified-depth circuit whose error remains below a user threshold.

The 17.9% depth reduction is measured on logical rounds after verified reordering and fusion, yet the evaluation remains confined to small-suite circuits; scaling the certificate-checked pipeline to circuits with hundreds of logical qubits will require both larger verified magic-state factories and tighter integration with surface-code lattice surgery schedulers already under active development.

Next steps include extending the mechanization to lattice-surgery primitives and embedding the certificate generator inside existing compilers such as t|ket> or Qiskit so that depth bounds become part of routine compilation rather than post-hoc verification.