Spectral Gap Optimization for Enhanced Adiabatic State Preparation.

Area of Science:

• Quantum Many-Body Physics
• Quantum Information Science
• Computational Physics

Background:

• Preparing nontrivial quantum states is essential for studying quantum many-body physics.
• Adiabatic quantum algorithms are a common method, but are limited by the spectral gap.
• Tensor network states (TNSs) offer a powerful framework for representing complex quantum states.

Purpose of the Study:

• To propose an efficient method for adiabatically preparing tensor network states (TNSs).
• To overcome the spectral gap limitation in adiabatic quantum algorithms.
• To demonstrate the applicability of the method to various TNSs and quantum states.

Main Methods:

• Develop an efficient adiabatic algorithm for TNS preparation.
• Maximize the spectral gap by optimizing the parent Hamiltonian construction.
• Apply the method to random TNSs in one dimension, AKLT states, and GHZ states.
• Extend Hamiltonian optimization to both injective and non-injective tensors, utilizing symmetries.

Main Results:

• Successfully demonstrated an efficient adiabatic algorithm for preparing TNSs.
• Showcased the method's effectiveness on diverse examples including random TNSs, AKLT, and GHZ states.
• Proved the Hamiltonian optimization's applicability to both injective and non-injective tensors.

Conclusions:

• The proposed efficient adiabatic algorithm significantly enhances the preparation of TNSs.
• This method provides a robust approach for generating complex quantum states relevant to many-body physics.
• The Hamiltonian optimization technique offers flexibility and broad applicability in quantum state preparation.