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Improvements to Quantum Interior Point Method for Linear Optimization
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DOI：10.1145/3702244.png)
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摘要
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Quantum linear system algorithms (QLSAs) have the potential to speed up Interior Point Methods (IPMs). 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 fewer 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.
Keyword:
Quantum linear system algorithm
quantum interior point method
linear optimization
iterative refinement
preconditioning
期刊
A
IF:
6.8
论文数:
539
被引数:
508
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