Stab-QRAM: An All-Clifford Quantum Random Access Memory for Special Data

• URL: http://arxiv.org/abs/2509.26494v2
• Date: Sun, 05 Oct 2025 01:29:26 GMT
• Title: Stab-QRAM: An All-Clifford Quantum Random Access Memory for Special Data
• Authors: Guangyi Li, Yu Gan, Zeguan Wu, Xueyue Zhang, Zheshen Zhang, Junyu Liu,
• Abstract summary: We introduce the Stabilizer-QRAM (Stab-QRAM), a domain-specific architecture tailored for data.<n>We show that Stab-QRAM achieves an optimal logical circuit depth of $O(log N)$ for $N$ data items, matching its $O(log N)$ space complexity.<n>This design completely circumvents the non-Clifford bottleneck, eliminating the need for costly magic state distillation.
• Score: 9.722458605511436
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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