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Sample Complexity of Device-Independently Certified "Quantum Supremacy".

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Certifying quantum computational advantage is challenging. Demonstrating quantum superiority requires exponentially many samples for non-interactive verification of approximate sampling tasks like boson sampling.

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Area of Science:

  • Quantum Computing
  • Computational Complexity Theory
  • Quantum Information Science

Background:

  • Quantum computing promises computational advantages over classical computers.
  • Approximate sampling tasks like boson sampling are candidates for demonstrating this advantage.
  • Verifying the correct implementation of these quantum experiments is a critical challenge.

Purpose of the Study:

  • To investigate the feasibility of non-interactive certification for approximate quantum sampling.
  • To determine the sample complexity required for verifying quantum computational advantage claims.
  • To analyze the limitations of classical verification methods for quantum sampling experiments.

Main Methods:

  • Theoretical analysis of sampling distributions in quantum computing.
  • Development of hardness proofs for approximate sampling problems.
  • Investigation of the role of second moments in sampling distributions.
  • Examination of non-interactive verification protocols.

Main Results:

  • Any non-interactive certification from classical samples requires exponentially many uses of the quantum device for tasks like boson sampling, IQP, and random circuit sampling.
  • This exponential sample complexity holds for all sufficiently flat distributions.
  • The proofs leverage the property of small second moments in the sampling distributions.

Conclusions:

  • Verifying quantum computational advantage through approximate sampling is significantly harder than previously assumed.
  • Current non-interactive classical verification methods are insufficient for convincing demonstrations.
  • Future research may need to explore interactive protocols or alternative verification strategies.