AI 中文总结
研究一种维度饱和固定核心假设下的两量子三比特门分解，通过制定光滑映射给出局部通用性可验证证书，构造核心并分类辛作用，证明对称类结构障碍，评估超导核心，建立局部通用性，区分精确证书与数值证据。
AI 中文摘要
我们研究了一种维度饱和的固定核心假设，其中固定的、不可调谐的两量子三比特核心\(K\in SU(9)\)的四个副本与来自\(L = SU(3)\otimes SU(3)\)的五个可调局部层交错排列。由于\(\dim SU(9)=80\)且\(5\dim L = 80\)，这是参数计数未排除的最短固定核心架构。我们制定了光滑映射\(\Phi_K:L^5\to SU(9)\)，并使用其右平凡化微分给出局部通用性的可验证证书。我们构造了一个明确的克利福德字核心，其泡利标签分裂使恒等点微分成为精确等距，并对满足相同分裂标准的所有2304个辛作用进行分类。我们还证明了一个重要对称类的结构障碍：每个复对称核心\(K = K^{T}\)，包括在所选计算基中由与时间无关的实对称哈密顿量生成的每个核心，恒等点微分秩最多为78；因此，对于这样一个核心的任何满秩证书都必须在该点之外出现。然后，我们评估了由非对易、时间不对称驱动生成的受硬件启发的超导核心。直接计算验证了\(K_{\rm sc}\neq K_{\rm sc}^{\mathsf T}\)，并且在规定重启协议下测试的所有1000个哈尔随机目标中，该核心实现了\(F_{\rm avg}\ge 0.999\)。我们还报告了有利的采样雅可比秩、结构化目标和鲁棒性诊断。这些结果在参数计数最小、维度饱和深度上建立了局部通用性，有精确的克利福德证书，并辅以受硬件启发的数值案例研究。在整个过程中，我们将精确的局部证书与更广泛合成性能的数值证据分开。
英文摘要
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.
Comments31 pages, 10 figures
