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Experimental quantum computing to solve systems of linear equations.

X-D Cai1, C Weedbrook2, Z-E Su1

  • 1Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.

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Quantum computers offer an exponential speedup for solving linear systems of equations. This study demonstrates a quantum algorithm for solving 2x2 linear systems, showcasing its potential for scientific computing.

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Area of Science:

  • Quantum Computing
  • Computational Science
  • Linear Algebra

Background:

  • Solving linear systems is crucial in science and engineering.
  • Classical algorithms face scalability issues with large datasets.
  • Quantum algorithms promise exponential speedups for linear systems.

Purpose of the Study:

  • To experimentally realize the simplest instance of a quantum algorithm for solving linear systems.
  • To demonstrate the feasibility of quantum computation for linear algebra tasks.
  • To validate the principles of quantum-enhanced linear system solvers.

Main Methods:

  • Implementation of a quantum algorithm on a quantum computer.
  • Utilizing four qubits and four controlled logic gates.
  • Solving 2x2 linear equations with various input vectors.

Main Results:

  • Successful execution of the quantum algorithm for 2x2 linear systems.
  • Demonstration of the core subroutines required for the algorithm.
  • Validation of the quantum approach for solving linear equations.

Conclusions:

  • The experimental realization confirms the working principle of the quantum linear system algorithm.
  • This work provides a foundational step towards quantum advantage in scientific computing.
  • Quantum computers show promise for efficiently tackling complex linear systems.