Quantum IPMs for Linear Optimization

Mohammadisiahroudi, Mohammadhossein; Terlaky, Tamás

doi:10.1007/978-3-030-54621-2_851-1

Encyclopedia of Optimization 2023

DOI: 10.1007/978-3-030-54621-2_851-1

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Quantum IPMs for Linear Optimization

Mohammadhossein Mohammadisiahroudi,

Tamás Terlaky

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2024

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Cited by 1 publication

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Improvements to Quantum Interior Point Method for Linear Optimization

Mohammadisiahroudi,

Wu,

Augustino

et al. 2024

ACM Transactions on Quantum Computing

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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.

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Improvements to Quantum Interior Point Method for Linear Optimization

Mohammadisiahroudi,

Wu,

Augustino

et al. 2024

ACM Transactions on Quantum Computing

View full text Add to dashboard Cite

show abstract

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Quantum IPMs for Linear Optimization

Cited by 1 publication

References 15 publications

Improvements to Quantum Interior Point Method for Linear Optimization

Improvements to Quantum Interior Point Method for Linear Optimization

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