Parent Hamiltonian Reconstruction via Inverse Quantum Annealing

Area of Science:

• Quantum Physics
• Quantum Information Science
• Computational Physics

Background:

• Finding a parent Hamiltonian for a given quantum state is crucial for quantum technologies.
• Existing methods face challenges in efficiency and scalability.

Purpose of the Study:

• Introduce a numerical method, inverse quantum annealing, to efficiently find parent Hamiltonians.
• Demonstrate the method's applicability on relevant quantum models.

Main Methods:

• Employing artificial inverse dynamics via a slow deformation of quantum states.
• Utilizing a projection onto local operators and requiring only local expectation values.
• Inspired by quantum annealing principles for adiabatic Hamiltonian evolution.

Main Results:

• The inverse quantum annealing method efficiently generates an approximate parent Hamiltonian.
• The degree of locality in the resulting Hamiltonian depends on state correlations.
• Successful application to the Kitaev fermionic chain and quantum Ising chain models.

Conclusions:

• Inverse quantum annealing provides a viable numerical approach for constructing parent Hamiltonians.
• The method's efficiency and reliance on local observables make it promising for quantum technologies.
• Further exploration of its capabilities on complex quantum systems is warranted.