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Quantum Algorithms for Testing Hamiltonian Symmetry.

Margarite L LaBorde1, Mark M Wilde1

  • 1Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA.

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|October 28, 2022
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Summary
This summary is machine-generated.

We developed quantum algorithms to detect symmetries in Hamiltonians, crucial for understanding conserved quantities in quantum physics. These algorithms were successfully tested on current quantum computers, validating their effectiveness.

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Area of Science:

  • Quantum Physics
  • Quantum Computing
  • Computational Physics

Background:

  • Symmetries in quantum Hamiltonians are fundamental, directly linking to conserved quantities in physical systems.
  • Understanding and verifying these symmetries is essential for advancing quantum mechanics and related fields.

Purpose of the Study:

  • To propose novel quantum algorithms for testing Hamiltonian symmetries with respect to a group.
  • To demonstrate the correspondence between established quantum mechanical symmetry expressions and algorithm acceptance probabilities.

Main Methods:

  • Development of quantum algorithms specifically designed for symmetry detection in Hamiltonians.
  • Experimental execution of a proposed symmetry-testing algorithm on existing quantum computing hardware.
  • Analysis of algorithm acceptance probabilities to confirm symmetry properties.

Main Results:

  • The proposed quantum algorithms effectively test for Hamiltonian symmetries.
  • A direct correlation was established between theoretical Hamiltonian symmetry and the practical outcomes (acceptance probabilities) of the quantum algorithms.
  • Successful demonstration on current quantum computers for both symmetric and asymmetric Hamiltonians.

Conclusions:

  • Quantum algorithms offer a viable and effective method for verifying Hamiltonian symmetries.
  • This work bridges theoretical concepts of symmetry in quantum mechanics with practical quantum computation.
  • The developed algorithms pave the way for more complex symmetry analyses in quantum systems.