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When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...
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Spectral Gap Optimization for Enhanced Adiabatic State Preparation.

Kshiti Sneh Rai1,2, Jin-Fu Chen1,2, Patrick Emonts1,2,3,4

  • 1Universiteit Leiden, Instituut-Lorentz, P.O. Box 9506, 2300 RA Leiden, The Netherlands.

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Summary
This summary is machine-generated.

We present an efficient adiabatic algorithm to prepare complex quantum states using tensor network states (TNSs). This method maximizes the spectral gap, overcoming limitations of current quantum algorithms for many-body physics.

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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.