Quantum random access memories (QRAMs) are pivotal for data-intensive quantum algorithms, but existing general-purpose and domain-specific architectures are hampered by a critical bottleneck: a heavy reliance on non-Clifford gates (e.g., T-gates), which are prohibitively expensive to implement fault-tolerantly. To address this challenge, we introduce the Stabilizer-QRAM (Stab-QRAM), a domain-specific architecture tailored for data with an affine Boolean structure ($f(\mathbf{x}) = A\mathbf{x} + \mathbf{b}$ over $\mathbb{F}_2$), a class of functions vital for optimization, time-series analysis, and quantum linear systems algorithms. We demonstrate that the gate interactions required to implement the matrix $A$ form a bipartite graph. By applying K\"{o}nig's edge-coloring theorem to this graph, we prove that Stab-QRAM achieves an optimal logical circuit depth of $O(\log N)$ for $N$ data items, matching its $O(\log N)$ space complexity. Critically, the Stab-QRAM is constructed exclusively from Clifford gates (CNOT and X), resulting in a zero $T$-count. This design completely circumvents the non-Clifford bottleneck, eliminating the need for costly magic state distillation and making it exceptionally suited for early fault-tolerant quantum computing platforms. We highlight Stab-QRAM's utility as a resource-efficient oracle for applications in discrete dynamical systems, and as a core component in Quantum Linear Systems Algorithms, providing a practical pathway for executing data-intensive tasks on emerging quantum hardware.

翻译：量子随机存取存储器（QRAM）对于数据密集型量子算法至关重要，但现有的通用和专用架构都受到一个关键瓶颈的制约：严重依赖非Clifford门（例如T门），而这些门在容错实现上成本极高。为应对这一挑战，我们引入了Stabilizer-QRAM（Stab-QRAM），这是一种专为具有仿射布尔结构（在$\mathbb{F}_2$上$f(\mathbf{x}) = A\mathbf{x} + \mathbf{b}$）的数据设计的专用架构，此类函数对于优化、时间序列分析和量子线性系统算法至关重要。我们证明了实现矩阵$A$所需的门相互作用形成一个二分图。通过将K\"{o}nig边着色定理应用于该图，我们证明了对于$N$个数据项，Stab-QRAM实现了$O(\log N)$的最优逻辑电路深度，与其$O(\log N)$的空间复杂度相匹配。至关重要的是，Stab-QRAM完全由Clifford门（CNOT和X）构建，因此T门计数为零。该设计完全规避了非Clifford瓶颈，无需昂贵的魔术态蒸馏，使其特别适合早期的容错量子计算平台。我们强调了Stab-QRAM作为离散动力系统应用中资源高效的预言机，以及作为量子线性系统算法核心组件的实用性，为在新兴量子硬件上执行数据密集型任务提供了一条实用途径。