多量子比特条件相位门的结构化哈密顿量学习
Structured Hamiltonian Learning for Multiqubit Conditional Phase Gates
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- International Quantum Academy（国际量子学院）
- Shenzhen Branch, Hefei National Laboratory（合肥国家实验室深圳分部）
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中文总结 AI 辅助
针对多量子比特条件相位门，提出结构化哈密顿量学习方法，通过Ramsey测量和Walsh变换重建误差生成器，利用布尔-莫比乌斯不变量实现全局等价性判定，实验验证了高精度与全局审计有效性。
中文摘要 AI 辅助
准确测量预期的条件相位本身并不能将多量子比特相位门置于其声明的广义门等价类中。我们将诊断问题视为在已知基下对对角成功块的结构化哈密顿量学习：对连通图上的Ramsey测量重建目标相对相位图；随后Walsh变换在选定的对数分支中产生每周期频闪误差生成器，其分支相关系数单独无法决定全局等价性。对于权重至多为m的对角Pauli-Z dressing，我们从乘法布尔-莫比乌斯不变量推导出精确的与分支无关的判据，在有限射击次数下转换为在预定容差和同时置信度下的通过/失败/未解决决策，与模型拒绝分离。对于共享控制的C^mZ门，圆形目标面对比度隔离每个预期的条件相位，然而一个支撑定理表明，一旦存在多个目标或外部旁观者，某些被禁止的相互作用对每个目标面都不可见。我们推导了任意整数相位对比度的Cramer-Rao界，恢复了均匀(m+1)体面的4^m尝试电路缩放，并量化了由可见性损失、预示存活、读出混淆和相关噪声引起的退化，而系统性偏差触发模型拒绝。种子模拟端到端实现了4M设置的多路复用采集：对于M=3,4,5在共同预算下，其平均相位图RMSE是单独编译的逐状态扫描的0.689-0.794倍，盲相互作用测试产生300/300全局审计拒绝，而目标面为1/300。这些结果在指定采集模型下估计对角成功块的误差生成器；它们不是未知基哈密顿量识别、任意通道断层扫描或硬件认证。
英文摘要
Accurate measurement of an intended conditional phase does not by itself place a multiqubit phase gate in its declared generalized-gate equivalence class. We cast the diagnosis as structured Hamiltonian learning of the diagonal successful block in a known basis: Ramsey measurements on a connected graph reconstruct a target-relative eigenphase map; a Walsh transform then yields the per-cycle stroboscopic error generator in a selected logarithm branch, whose branch-dependent coefficients alone cannot decide global equivalence. For diagonal Pauli-Z dressing of weight at most m we derive an exact branch-independent criterion from multiplicative Boolean-Mobius invariants, converted at finite shot counts into a pass/fail/unresolved decision under prespecified tolerances and simultaneous confidence, separate from model rejection. For shared-control C^mZ gates a circular target-face contrast isolates each intended conditional phase, yet a support theorem exhibits forbidden interactions invisible to every target face once multiple targets or external spectators are present. We derive a Cramer-Rao bound for arbitrary integer phase contrasts, recovering the 4^m attempted-circuit scaling of a uniform (m+1)-body face, and quantify degradation from visibility loss, heralded survival, readout confusion, and correlated noise, while systematic bias triggers model rejection. Seeded simulations implement the 4M-setting multiplexed acquisition end to end: for M=3,4,5 at a common budget its mean phase-map RMSE is 0.689-0.794 times a separately compiled statewise scan, and a blind-interaction test yields 300/300 global-audit rejections versus 1/300 for target faces. These results estimate the error generator of a diagonal successful block under a specified acquisition model; they are not unknown-basis Hamiltonian identification, arbitrary-channel tomography, or hardware certification.
