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This study introduces a classical algorithm for estimating quantum circuit properties. It efficiently handles complex circuits, making quantum computations more accessible.

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Area of Science:

  • Quantum Computing
  • Computational Complexity

Background:

  • Estimating expectation values of quantum circuits is crucial for quantum computation.
  • Current methods face challenges with complex circuit architectures and depths.

Purpose of the Study:

  • To develop a classical algorithm for efficient expectation value estimation.
  • To analyze the algorithm's performance across diverse quantum circuit types.

Main Methods:

  • A novel classical algorithm based on Pauli propagation.
  • Analysis of error bounds (ϵ) and failure probability (δ).
  • Assessment of computational complexity in relation to qubit count and circuit depth.

Main Results:

  • The algorithm achieves small error (ϵ) on most circuits, with a small failure fraction (δ).
  • Computational time is polynomial for constant ϵ, δ and quasipolynomial for smaller error bounds.
  • Demonstrates classical tractability for estimating observables in chaotic and scrambling quantum circuits.

Conclusions:

  • The proposed algorithm offers an efficient classical approach for analyzing quantum circuits.
  • This work broadens the scope of classically tractable quantum computations.
  • Applicable to all circuit architectures, including those with all-to-all connectivity.