Quantum Algorithms for Testing Hamiltonian Symmetry

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.