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This paper presents the Pauli-based Circuit Optimization, Analysis, andSynthesis Toolchain (PCOAST), a framework for quantum circuit optimizationsbased on the commutative properties of Pauli strings. Prior work hasdemonstrated that commuting Clifford gates past Pauli rotations can exposeopportunities for optimization in unitary circuits. PCOAST extends thatapproach by adapting the technique to mixed unitary and non-unitary circuitsvia generalized preparation and measurement nodes parameterized by Paulistrings. The result is the PCOAST graph, which enables novel optimizationsbased on whether a user needs to preserve the quantum state after executing thecircuit, or whether they only need to preserve the measurement outcomes.Finally, the framework adapts a highly tunable greedy synthesis algorithm toimplement 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 leadingquantum compilers, Qiskit and tket. We find that PCOAST reduces total gatecount by 32.53% and 43.33% on average, compared to to the best performanceachieved by Qiskit and tket respectively, two-qubit gates by 29.22% and 20.58%,and circuit depth by 42.02% and 51.27%.

PCOAST: A Pauli-based Quantum Circuit Optimization Framework