Modeling and Resource Optimization for Quantum Oracles

TL;DR

This paper introduces a formal model and an optimization algorithm for quantum oracles, reducing resource overhead and improving efficiency in quantum algorithms.

Contribution

It presents a Hierarchical Recursive Synthesis-Evaluation model and an Adaptive Space-depth Trade-off algorithm for resource-efficient quantum oracle design.

Findings

The ASDT algorithm reduces quantum circuit depth by 54%.

The model enables precise complexity analysis of quantum oracles.

The approach achieves optimal gate count under qubit constraints.

Abstract

Quantum computing has demonstrated its significant advantage over supercomputing for specific applications and shown promising prospect, such as machine learning, cryptography, finance, etc.. Quantum oracles are very common in many quantum algorithms and oracle resource consumption directly affects algorithm performance. However, existing oracle designs often exhibit high resource overhead and limited compatibility. Moreover, structured description tools and complexity analysis methods are lacked. In this work, we introduces a Hierarchical Recursive Synthesis-Evaluation (HRSE) model, enabling formal description and precise quantum gate complexity analysis of oracles. Based on this model, we propose an Adaptive Space-depth Trade-off (ASDT) algorithm for generating oracle structures under a fixed qubit constraint. We provide a theoretical proof showing that the ASDT algorithm achieves the optimal gate count for a given number of qubits. Experimental results show that the ASDT algorithm reduces the average quantum circuit depth by 53.99% compared with the W-cycle approach, with the number of variables being 10, 15, and 20, respectively.