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Role of Coherence for Quantum Computational Advantage.

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We introduce path coherence, a new measure for quantum computational advantage. This metric quantifies coherent interferences, enabling classical computers to simulate quantum computations more efficiently.

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Area of Science:

  • Quantum Computing
  • Computational Complexity
  • Quantum Information Theory

Background:

  • Quantifying quantum resources is crucial for distinguishing quantum from classical computation.
  • Entanglement, nonstabilizerness, and coherence are key quantum resources.
  • Coherence plays a significant role in achieving quantum computational advantage.

Purpose of the Study:

  • Introduce "path coherence" as a novel measure of coherent path interferences in quantum computation.
  • Establish a connection between path coherence and the difficulty of classical simulation of quantum systems.
  • Provide a new perspective on the role of coherence in quantum advantage.

Main Methods:

  • Utilize the sum-over-paths formalism to develop a classical algorithm.
  • Estimate quantum transition amplitudes using the developed classical algorithm.
  • Analyze the complexity scaling of the estimation algorithm with respect to path coherence.

Main Results:

  • Developed a classical algorithm for estimating quantum transition amplitudes.
  • Demonstrated that the algorithm's complexity scales directly with path coherence.
  • Showcased path coherence as a relevant measure for quantum computational advantage.

Conclusions:

  • Path coherence offers a new perspective on the role of coherence in quantum advantage.
  • The developed classical algorithm has practical applications for simulating quantum computations.
  • This work bridges fundamental quantum information theory with practical computational challenges.