Improvements to Quantum Interior Point Method for Linear Optimization
Author(s)
Mohammadisiahroudi, Mohammadhossein
Wu, Zeguan
Augustino, Brandon
Carr, Arielle
Terlaky, Tam?s
Date Issued
October 29, 2024
Journal
ACM Transactions on Quantum Computing
Publisher
ACM
Citation
Mohammadisiahroudi, Mohammadhossein, Wu, Zeguan, Augustino, Brandon, Carr, Arielle and Terlaky, Tam?s. 2024. "Improvements to Quantum Interior Point Method for Linear Optimization." ACM Transactions on Quantum Computing.
Version
Final published version
Abstract
Quantum linear system algorithms (QLSA) have the potential to speed up Interior Point Methods (IPM). However, a major bottleneck is the inexactness of quantum Tomography to extract classical solutions from quantum states. In addition, QLSAs are sensitive to the condition number, and this sensitivity is exacerbated when the Newton systems arising in IPMs converge to a singular matrix. Recently, an Inexact Feasible Quantum IPM (IF-QIPM) has been developed that addresses the inexactness of QLSAs. However, this method requires a large number of gates and qubits to be implemented. Here, we propose a new IF-QIPM using the normal equation system, which requires less number of gates and qubits. To mitigate the sensitivity to the condition number and other input data-related parameters, we use preconditioning coupled with iterative refinement to obtain better complexity. Finally, we demonstrate the effectiveness of our approach on IBM Qiskit simulators.
MIT Department
Sloan School of Management
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3702244
