This study introduces a new optimization model and a branch-and-cut approach for synthesizing optimal quantum circuits for reversible Boolean functions, which are pivotal components in quantum algorithms. Although heuristic algorithms have been extensively explored for quantum circuit synthesis, research on exact counterparts remains relatively limited. However, the need to design quantum circuits with guaranteed optimality is increasing, especially for improving computational fidelity on noisy intermediate-scale quantum devices. This study presents mathematical optimization as a viable option for optimal synthesis, with the potential to accommodate practical considerations arising in fast-evolving quantum technologies. We set a demonstrative problem to implement reversible Boolean functions using high-level gates known as multiple control Toffoli gates while minimizing a technology-based proxy called quantum cost—the number of low-level gates used to realize each high-level gate. To address this problem, we propose a discrete optimization model based on a multicommodity network and discuss potential future variations at an abstract level to incorporate technical considerations. A customized branch and cut is then developed upon different aspects of our model, including polyhedron integrality, surrogate constraints, and variable prioritization. Our experiments demonstrate the robustness of the proposed approach in finding cost-optimal circuits for all benchmark instances within a two-hour time frame. Furthermore, we present interesting intuitions from these experiments and compare our computational results with relevant studies, highlighting newly discovered circuits with the lowest quantum costs reported in this paper. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Quantum Computing. Funding: This research was supported by the Ministry of Science and Information and Communication Technology, South Korea [Grants 2017R1E1A1A0307098814 and 2020R1A4A307986411]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0562 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0562 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

The contribution of this article is twofold. First, we present Indexing by latent Dirichlet allocation (LDI), an automatic document indexing method. Many ad hoc applications, or their variants with smoothing techniques suggested in LDA‐based language modeling, can result in unsatisfactory performance as the document representations do not accurately reflect concept space. To improve document retrieval performance, we introduce a new definition of document probability vectors in the context of LDA and present a novel scheme for automatic document indexing based on LDA. Second, we propose an Ensemble Model (EnM) for document retrieval. EnM combines basic indexing models by assigning different weights and attempts to uncover the optimal weights to maximize the mean average precision. To solve the optimization problem, we propose an algorithm, which is derived based on the boosting method. The results of our computational experiments on benchmark data sets indicate that both the proposed approaches are viable options for document retrieval.

This paper proposes a new packet rate scheduling scheme for a non-real time data service over the uplink of a burst switching-based direct sequence code division multiple access (DS/CDMA) system to support the integrated voice/data service. We consider the most general form of optimization problem formulation to determine the optimal number of transmission-time groups along with their data rates, which minimize the average packet transmission delay. An ordered packet length-based group-wise transmission (OLGT) scheme is proposed as a simple heuristic solution approach to this problem and present some analytical results for performance comparison with other possible schemes.