  This paper presents the Pauli-based Circuit Optimization, Analysis, and
Synthesis Toolchain (PCOAST), a framework for quantum circuit optimizations
based on the commutative properties of Pauli strings. Prior work has
demonstrated that commuting Clifford gates past Pauli rotations can expose
opportunities for optimization in unitary circuits. PCOAST extends that
approach by adapting the technique to mixed unitary and non-unitary circuits
via generalized preparation and measurement nodes parameterized by Pauli
strings. The result is the PCOAST graph, which enables novel optimizations
based on whether a user needs to preserve the quantum state after executing the
circuit, or whether they only need to preserve the measurement outcomes.
Finally, the framework adapts a highly tunable greedy synthesis algorithm to
implement the PCOAST graph with a given gate set.
  PCOAST is implemented as a set of compiler passes in the Intel Quantum SDK.
In this paper, we evaluate its compilation performance against two leading
quantum compilers, Qiskit and tket. We find that PCOAST reduces total gate
count by 32.53% and 43.33% on average, compared to to the best performance
achieved by Qiskit and tket respectively, two-qubit gates by 29.22% and 20.58%,
and circuit depth by 42.02% and 51.27%.
