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  3. Provable And Verifiable Quantum Advantage In Sample Complexity.
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  3. Provable And Verifiable Quantum Advantage In Sample Complexity.

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View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces a quantum algorithm for complement sampling, efficiently finding elements in a complementary set. Quantum computation offers significant advantages over classical methods in sample complexity, especially for noisy intermediate-scale quantum devices.

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Area of Science:

  • Quantum Computing
  • Computational Complexity
  • Information Theory

Background:

  • Complement sampling involves obtaining a sample from a complementary subset given samples from a subset.
  • Classical algorithms require numerous samples for complement sampling, especially when subset sizes are large.

Purpose of the Study:

  • To develop a quantum algorithm for complement sampling.
  • To demonstrate quantum advantage in sample complexity compared to classical algorithms.
  • To explore the potential for noisy intermediate-scale quantum (NISQ) computer implementations.

Main Methods:

  • A simple quantum algorithm utilizing a single quantum sample (uniform superposition) was developed.
  • Analysis of the algorithm's success probability and comparison with classical sample complexity bounds.
  • Extension of results to prove average-case hardness.

    • Main Results:

    • The quantum algorithm achieves a 100% success probability for complement sampling when subset sizes are equal (K=N/2).
    • Classical algorithms require samples proportional to N for comparable success probability.
    • The quantum approach demonstrates the largest possible separation in sample complexity.

    Conclusions:

    • Quantum computation offers provable and verifiable advantages in sample complexity for complement sampling.
    • The algorithm is suitable for demonstration on NISQ computers.
    • Complement sampling provides a pathway to quantum advantage under the assumption of one-way functions.