GULPS: Two-Qubit Gate Synthesis via Linear Programming for Heterogeneous Instruction Sets

Abstract

Modern quantum hardware exposes heterogeneous two-qubit instruction sets through fractional, continuously parameterized, and per-pair native gates, but synthesis remains largely framed around CNOT and a small catalog of closed-form rules. We present \textbf{GULPS} (Global Unitary Linear Programming Synthesis), a two-qubit compiler that partitions synthesis into depth-$2$ segments and uses a linear program over quantum Littlewood--Richardson reachability inequalities to plant the intermediate invariants between them. Each segment becomes an independent low-dimensional least-squares fit, solved by a Gauss--Newton/Levenberg--Marquardt routine. On Haar-random two-qubit targets, GULPS is more than $500{\times}$ faster than the general-purpose synthesizers BQSKit and NuOp at strictly lower circuit cost. Against Qiskit's specialized \texttt{XXDecomposer} on $XX$-family ISAs, GULPS produces identical output circuits $3.9$--$9.2{\times}$ faster, compounding to $7$--$19{\times}$ on full-circuit transpilation. All decompositions reach the double-precision unitary-infidelity floor. As a byproduct, the continuous formulation yields a Haar-averaged lower bound on expected circuit cost, against which discrete calibration choices can be benchmarked. GULPS is distributed on PyPI and registers as a Qiskit translation-stage plugin.