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arXiv · 2509.26494

Stab-QRAM: A Clifford-Only Quantum Oracle for Affine Boolean Data

Guangyi Li·Yu Gan·Zeguan Wu·Xueyue Zhang·Zheshen Zhang·Junyu Liu
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Abstract

Oracle-based quantum algorithms require coherent evaluation of classical functions on superposed inputs, and in fault-tolerant architectures this cost is dominated by non-Clifford gates: generic lookup constructions incur $T$-counts that grow with the data size. Here we show that affine Boolean functions $f(\mathbf{x})=A\mathbf{x}+\mathbf{b}$ over $\mathbb{F}_2$ -- the algebraic core of parity checks, linear feedback shift registers, and cipher linear layers -- are exactly the functions admitting computational-basis-preserving Clifford oracles, and we develop this correspondence into Stab-QRAM, a compiler mapping a specification $(A,\mathbf{b})$ to an ancilla-free circuit of CNOT and $X$ gates with zero $T$-count. Via K\"{o}nig's edge-coloring theorem, the compiled schedule provably attains the minimum depth for its gate set. Case studies spanning Simon-type oracles, block-encodings of $X$-type coset operators, and syndrome extraction for CSS codes show one compiler serving the algorithm, primitive, and error-correction layers of the quantum stack.

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Guangyi Li, Yu Gan, Zeguan Wu, Xueyue Zhang, Zheshen Zhang, Junyu Liu. 2025-09-30. Stab-QRAM: A Clifford-Only Quantum Oracle for Affine Boolean Data. https://arxiv.org/abs/2509.26494

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