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We developed a Monte Carlo method to estimate quantum circuit outcome probabilities. The method

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Area of Science:

  • Quantum computing
  • Computational physics

Background:

  • Estimating outcome probabilities for quantum circuits is computationally challenging.
  • Classical algorithms struggle with the exponential complexity of quantum state evolution.

Purpose of the Study:

  • To present a novel method for efficiently estimating quantum circuit outcome probabilities.
  • To establish a connection between computational efficiency and a resource measure of quantum states.

Main Methods:

  • Utilizing Monte Carlo sampling techniques.
  • Applying these techniques to a quasiprobability representation of quantum states.
  • Quantifying circuit negativity using the 1-norm of the quasiprobability distribution.

Main Results:

  • The estimation accuracy converges to the true quantum probability.
  • Convergence rate is determined by the circuit's total negativity.
  • Efficient convergence is achieved if negativity grows polynomially with circuit size.

Conclusions:

  • Negativity serves as a crucial resource measure for quantum computation.
  • The proposed method offers an efficient approach to estimate quantum probabilities.
  • This work bridges the gap between resource theory and computational complexity in quantum computing.