Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition

• URL: http://arxiv.org/abs/2607.24129v1
• Date: Mon, 27 Jul 2026 08:12:43 GMT
• Title: Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition
• Abstract summary: We study a dimension-saturating fixed-core ansatz in which four copies of a fixed, non-tunable two-qutrit core are interleaved with five adjustable local layers.<n>This is the shortest fixed-core architecture not excluded by parameter counting.<n>We then assess a hardware-motivated superconducting core generated by a noncommuting, temporally asymmetric drive.
• Score: 6.151100037929983
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study a dimension-saturating fixed-core ansatz in which four copies of a fixed, non-tunable two-qutrit core $K\in SU(9)$ are interleaved with five adjustable local layers from $L=SU(3)\otimes SU(3)$. Since $\dim SU(9)=80$ and $5\dim L=80$, this is the shortest fixed-core architecture not excluded by parameter counting. We formulate the smooth map $Φ_K:L^5\to SU(9)$ and use its right-trivialized differential to give verifiable certificates for local universality. We construct an explicit Clifford-word core whose Pauli-label splitting makes the identity-point differential an exact isometry, and we classify all 2304 symplectic actions satisfying the same splitting criterion. We also prove a structural obstruction for an important symmetry class: every complex-symmetric core $K=K^{T}$, including every core generated by a time-independent real-symmetric Hamiltonian in the chosen computational basis, has identity-point differential rank at most 78; hence any full-rank certificate for such a core must occur away from that point. We then assess a hardware-motivated superconducting core generated by a noncommuting, temporally asymmetric drive. Direct calculation verifies $K_{\rm sc}\neq K_{\rm sc}^{\mathsf T}$, and the core achieves $F_{\rm avg}\ge 0.999$ for all 1000 Haar-random targets tested under the stated restart protocol. We also report favorable sampled Jacobian-rank, structured-target, and robustness diagnostics. These results establish local universality at the parameter-counting-minimal, dimension-saturating depth, with an exact Clifford certificate complemented by a hardware-motivated numerical case study. Throughout, we separate exact local certificates from numerical evidence for broader synthesis performance.

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