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We developed a hybrid classical-quantum solver for linear equations, utilizing quantum random walks for efficient computation on quantum systems. This approach is robust and ready for machine learning applications.

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Area of Science:

  • Quantum Computing
  • Computational Mathematics
  • Machine Learning

Background:

  • Solving systems of linear equations is fundamental in many scientific and engineering disciplines.
  • Existing classical methods can be computationally intensive for large-scale problems.
  • Quantum computing offers potential for speedups in solving specific mathematical problems.

Purpose of the Study:

  • To propose and demonstrate a realistic hybrid classical-quantum linear solver.
  • To leverage quantum random walks for efficient linear equation solving.
  • To assess the feasibility and applicability of the algorithm on current quantum hardware.

Main Methods:

  • Development of a hybrid algorithm combining classical and quantum processing.
  • Implementation of a quantum random walk on a quantum circuit.
  • Utilizing Qiskit for simulation and execution on IBM Q systems.
  • Analysis of algorithm performance in terms of time complexity and qubit requirements.

Main Results:

  • Demonstrated feasibility of the hybrid solver on IBM Q systems.
  • The quantum random walk component runs in O(N log N) time.
  • The quantum circuit requires only O(log N) qubits.
  • The algorithm handles classical input and output, ensuring accessibility.
  • The solver exhibits robustness against noise.

Conclusions:

  • The proposed hybrid solver is a practical approach for specific linear systems.
  • The algorithm's efficiency and noise robustness make it suitable for near-term applications.
  • Readiness for implementation in fields like machine learning is highlighted.