  The quantum simulation kernel is an important subroutine appearing as a very
long gate sequence in many quantum programs. In this paper, we propose
Paulihedral, a block-wise compiler framework that can deeply optimize this
subroutine by exploiting high-level program structure and optimization
opportunities. Paulihedral first employs a new Pauli intermediate
representation that can maintain the high-level semantics and constraints in
quantum simulation kernels. This naturally enables new large-scale
optimizations that are hard to implement at the low gate-level. In particular,
we propose two technology-independent instruction scheduling passes, and two
technology-dependent code optimization passes which reconcile the circuit
synthesis, gate cancellation, and qubit mapping stages of the compiler.
Experimental results show that Paulihedral can outperform state-of-the-art
compiler infrastructures in a wide-range of applications on both near-term
superconducting quantum processors and future fault-tolerant quantum computers.
