Modeling and Resource Optimization for Quantum Oracles
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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BibTeX
@misc{li2026modeling,
title = {{Modeling and Resource Optimization for Quantum Oracles}},
author = {Zhihang Li and Bo Zhao and Chuanbing Han and Jie Zhao and Jinchen Xu and Guoqiang Shu and Yimin Gao and Woji He and Zheng Shan},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.21380},
eprint = {2605.21380},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.21380},
note = {CC0},
}
RIS
TY - UNPB
TI - Modeling and Resource Optimization for Quantum Oracles
AU - Zhihang Li
AU - Bo Zhao
AU - Chuanbing Han
AU - Jie Zhao
AU - Jinchen Xu
AU - Guoqiang Shu
AU - Yimin Gao
AU - Woji He
AU - Zheng Shan
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2605.21380
UR - https://arxiv.org/abs/2605.21380
AB - 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.
ER -