Design Method of Meta Operators Based on Equivalence Class Distribution

Abstract

Abstract Currently, there are many physical systems for quantum computing and to adapt to the physical characteristics of different systems, engineers have designed different basic gate groups for gate circuit calculation models. The quantum algorithm realizes the evolution of the quantum state by applying unitary operators to the quantum states, and the results are obtained by measuring the outputs. These operators will be done in the corresponding physical system by compiling and decomposing into hardware supported basic gates. Universal fundamental gates can construct all quantum algorithms, but their computational efficiency is limited. Drawing on the idea of meta operators in classical machine learning, by constructing a deep learning framework for deep learning models, the common computational logic of operators in different deep learning frameworks is abstracted as ‘meta operators’ [1, 2]. This article aims to study and propose the common computational logic of quantum computing with geometric equivalence class distribution methods, using the volume size of the equivalence class space as a performance indicator for meta operators and identifying the optimal meta operators to optimize the depth of the circuits in the experiments. Which proves the effectiveness of the design method proposed and provides solutions for quantum circuit optimization and dedicated gate design.