PSF-Zero: An Analytic Two-Qubit Gate Synthesizer Combined with a Verified, Ordering-Aware Layout Search for Quantum Circuit Transpilation

We present PSF-Zero, a two-part quantum circuit compiler consisting of (1) an analytic two-qubit gate synthesizer based on the Cartan (KAK) decomposition, implemented as a compiled Rust core, and (2) a qubit layout search built around a specific ordering strategy shown effective in a companion paper. On a fixed 15-qubit, dense-pair-block circuit family, the gate synthesizer reproduces Qiskit's own output to a fidelity of 1.000000000000 at small scale and achieves a 7.0–9.3x cumulative speedup over Qiskit's default optimization_level=3 synthesis path across independently repeated 10,000-iteration measurements; we report the variance of this speedup honestly, including a 34–54x reduction in timing variance observed between two measurement sessions whose cause we investigated with the actual source diff from both sessions and could not identify. The layout search, verified through the public compile_for_hardware() entry point rather than as an isolated component, finds a valid embedding on 26 of 26 saturated test instances—up from 0 of 26 before a feasibility-check defect we found and fixed—with all 26 outputs independently verified structurally valid (zero coupling-map violations) and, at small scale, unitary-equivalent to the input circuit to machine precision (minimum fidelity 0.999999999999994 across 36 independent checks). We further verify the same layout search on two topologies distinct from the square grids used in development, including one (brick) on which the search's own earlier ordering strategies had previously found nothing at all. We report every defect found in the course of this verification, including one whose root cause we mischaracterized in an earlier stage of this investigation and later corrected, and one inconsistency in our own reported timing figures that we found and correct in this paper. All code, raw data, and the complete chronological verification record are public.