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Variational algorithms for linear algebra.

Xiaosi Xu1, Jinzhao Sun2, Suguru Endo3

  • 1Center on Frontiers of Computing Studies, Department of Computer Science, Peking University, Beijing 100871, China; Department of Materials, University of Oxford, Oxford OX1 3PH, UK.

Science Bulletin
|January 19, 2023
PubMed
Summary
This summary is machine-generated.

We developed variational quantum algorithms for solving linear algebra tasks on current noisy quantum computers. These algorithms translate problems into finding ground states, achieving high fidelity on real quantum hardware.

Keywords:
Linear algebraMatrix multiplicationQuantum computingQuantum simulationVariational quantum eigensolver

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Area of Science:

  • Quantum Computing
  • Quantum Algorithms
  • Computational Linear Algebra

Background:

  • Existing quantum algorithms for linear algebra demand fault-tolerant quantum computers.
  • Noisy intermediate-scale quantum (NISQ) devices present limitations for complex quantum computations.

Purpose of the Study:

  • To propose variational quantum algorithms for linear algebra tasks suitable for NISQ devices.
  • To demonstrate the translation of linear algebra problems into finding ground states of Hamiltonians.

Main Methods:

  • Developed variational quantum algorithms for solving linear systems and matrix-vector multiplication.
  • Introduced Hamiltonian morphing and adaptive ansatz for efficient ground state finding.
  • Incorporated solution verification methods.

Main Results:

  • Solutions for linear systems and matrix-vector multiplication mapped to ground states of constructed Hamiltonians.
  • Algorithm demonstrated effectiveness for sparse matrices, applicable to machine learning and optimization.
  • Achieved 99.95% solution fidelity on an IBM quantum cloud device.

Conclusions:

  • Variational quantum algorithms offer a viable approach for linear algebra on NISQ devices.
  • The proposed methods, including Hamiltonian morphing, enhance efficiency and applicability.
  • Successful implementation on quantum hardware validates the approach for practical applications.