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arXiv · 2605.21380

Modeling and Resource Optimization for Quantum Oracles

Zhihang Li·Bo Zhao·Chuanbing Han·Jie Zhao·Jinchen Xu·Guoqiang Shu·Yimin Gao·Woji He·Zheng Shan
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Abstract

Quantum oracles are fundamental building blocks of many quantum algorithms, and their resource consumption directly affects performance, yet structured description and complexity analysis for their composition are still lacking. In this paper, we introduce the Framework for Oracle Recursion Modeling (FORM), a unified formal abstraction of multi-function composition in quantum oracles: it provides a structured description of the composition layer, makes its gate complexity exactly computable, and turns oracle design into an optimizable tree-construction problem. Based on this model, we propose the ShallowGrow algorithm, which constructs an oracle structure under a given ancilla budget and provably minimizes the number of function evaluations. On Boolean quadratic equation systems, ShallowGrow reduces Qiskit-measured circuit depth by 54.1% on average relative to the state-of-the-art W-cycle construction, with consistent reductions on the EPFL and ISCAS85 combinational logic networks under scarce ancilla budgets. Furthermore, pebbling-based syntheses trade space against time within the logic network of a function; ShallowGrow extends this trade-off across functions, and integrated with their published circuits it reduces the ancillary qubits of a complete oracle from one per constraint function to logarithmically many. With half as many ancillas as constraint functions, the T-count falls by a factor of 7.9 to 32 relative to the W-cycle-based construction.

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Zhihang Li, Bo Zhao, Chuanbing Han, Jie Zhao, Jinchen Xu, Guoqiang Shu, Yimin Gao, Woji He, Zheng Shan. 2026-08-30. Modeling and Resource Optimization for Quantum Oracles. https://arxiv.org/abs/2605.21380

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