Assessing the feasibility of quantum learning algorithms for noisy linear problems
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View abstract on PubMed
Summary
This summary is machine-generated.This study enhances quantum algorithms for noisy linear problems, extending quantum Fourier transform applicability. It also reveals efficient classical algorithms for specific learning with errors problems using quantum samples.
Area Of Science
- Quantum computing
- Cryptography
- Computational complexity
Background
- Existing quantum algorithms for noisy linear problems rely on specific assumptions.
- The ring learning with errors problem is a key challenge in this area.
- Previous work established polynomial-time quantum algorithms for noisy linear problems with quantum samples.
Purpose Of The Study
- To reexamine quantum algorithms for noisy linear problems.
- To extend the applicability of the quantum Fourier transform to the ring learning with errors problem.
- To investigate the existence of efficient classical algorithms for related problems.
Main Methods
- Reexamination of existing quantum algorithms under standard assumptions.
- Application of quantum Fourier transform techniques.
- Analysis of classical algorithms for specific lattice-based problems.
Main Results
- Extended applicability of the quantum Fourier transform to the ring learning with errors problem.
- Demonstrated efficient classical algorithms for short integer solution and size-reduced learning with errors problems when quantum samples are provided.
Conclusions
- The findings broaden the scope of quantum algorithms for noisy linear problems.
- Efficient classical solutions are possible for certain learning with errors variants under specific conditions.
- This work bridges quantum and classical approaches to solving complex computational problems.
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