用于无锚定近似 MUB 优化的可重现软件工作流程：六维案例研究
A Reproducible Software Workflow for Unanchored Approximate MUB Optimization: A Case Study in Dimension Six
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中文总结 AI 辅助
该研究提出可重现软件工作流程，用李代数酉参数化在任意维度优化 AMUB 配置，以六维为例进行研究，恢复精确三基配置等，还在量子硬件上检查执行情况，提供了探索 AMUB 景观的框架及对相关挑战的初步评估。
中文摘要 AI 辅助
我们提出了一种可重现的、参数驱动的软件工作流程，用于使用李代数酉参数化在任意维度 d 中优化近似相互无偏基（AMUB）配置。该工作流程设计用于在 CPU、Apple MPS、支持 CUDA 的 GPU 和 HPC 后端上进行便携式执行，使用泰勒级数矩阵指数层作为加速器兼容途径。作为六维案例研究，我们在 complex128 和 complex64 算法中针对基计数 n = 3、4、5、6 跨 100 个随机种子优化无锚定配置。该工作流程恢复了精确的三基配置，识别出一种反复出现的四基部分精确的中心和三角形结构，并且在主要容差下的报告活动中未找到 n = 5 或 n = 6 的近似精确对。作为硬件执行检查，我们将代表性的 d = 6、n = 4 过渡酉矩阵嵌入到三量子比特 8x8 酉矩阵中，并使用子空间后选择在 156 量子比特的 Heron 处理器 ibm - marrakesh 上执行所得电路。测量的 QPU 成对损失主要由约 0.02 - 0.08 的硬件和编译噪声底限主导，与平均 37 个原生 CZ 门的编译电路相关，这模糊了经典近似精确对和有缺陷对之间的区别。结果为探索 AMUB 景观提供了一个可重现的计算框架，同时对在当前量子硬件上执行优化的六维酉矩阵所涉及的挑战进行了初步评估。
英文摘要
We present a reproducible, parameter-driven software workflow for optimizing approximate mutually unbiased basis (AMUB) configurations in arbitrary dimensions d using a Lie-algebra unitary parameterization. The workflow is designed for portable execution across CPU, Apple MPS, CUDA-capable GPU, and HPC backends, using a Taylor-series matrix exponential layer as an accelerator compatibility pathway. As a dimension-six case study, we optimize unanchored configurations across 100 random seeds for basis counts n = 3, 4, 5, 6 in complex128 and complex64 arithmetic. The workflow recovers exact three-basis configurations, identifies a recurrent four-basis partial-exact hub-and-triangle structure, and finds no near-exact pairs for n = 5 or n = 6 in the reported campaigns under the primary tolerance. As a hardware-execution check, we embed the representative d = 6, n = 4 transition unitaries into three-qubit 8x8 unitaries and execute the resulting circuits on the 156-qubit Heron processor ibm-marrakesh using subspace post-selection. The measured QPU pairwise losses are dominated by a hardware and compilation noise floor of approximately 0.02-0.08, associated with compiled circuits averaging 37 native CZ gates, which obscures the distinction between classically near-exact and defective pairs. The results provide a reproducible computational framework for exploring AMUB landscapes, together with an initial assessment of the challenges involved in executing optimized dimension-six unitaries on current quantum hardware.
