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Hybrid quantum linear equation algorithm and its experimental test on IBM Quantum Experience.

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This study introduces a hybrid quantum algorithm that improves upon the Harrow-Hassidim-Lloyd (HHL) algorithm for solving linear equations. The new method reduces circuit depth and shows higher accuracy in experimental tests.

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Area of Science:

  • Quantum computing
  • Quantum algorithms
  • Linear algebra

Background:

  • Solving systems of linear equations is a fundamental problem in science and engineering.
  • The Harrow-Hassidim-Lloyd (HHL) algorithm offers a quantum approach to this problem, but with limitations in circuit depth.
  • Quantum phase estimation is a key subroutine in many quantum algorithms, including HHL.

Purpose of the Study:

  • To propose a novel hybrid quantum algorithm for solving systems of linear equations.
  • To reduce the circuit depth of the original Harrow-Hassidim-Lloyd (HHL) algorithm.
  • To experimentally validate the performance and accuracy of the proposed hybrid algorithm.

Main Methods:

  • Development of a hybrid quantum algorithm integrating classical feed-forward with quantum phase estimation.
  • Implementation and testing of the algorithm on a four-qubit system using IBM Quantum Experience.
  • Comparison of the hybrid algorithm's results with the standard HHL algorithm.

Main Results:

  • The hybrid algorithm successfully solves systems of linear equations.
  • A reduction in circuit depth compared to the original HHL algorithm was achieved.
  • Experimental results demonstrated higher accuracy for the hybrid algorithm on specific linear systems.

Conclusions:

  • The proposed hybrid quantum algorithm is an effective enhancement of the HHL algorithm.
  • Classical information feed-forward can optimize quantum algorithms by reducing circuit depth.
  • The experimental validation confirms the practical applicability and improved performance of the hybrid approach.