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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Fourier transform for fermionic systems and the spectral tensor network.

Andrew J Ferris1

  • 1Département de Physique, Université de Sherbrooke, Québec J1K 2R1, Canada; ICFO-Institut de Ciencies Fotoniques, Parc Mediterrani de la Tecnologia, 08860 Barcelona, Spain; and Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany.

Physical Review Letters
|July 18, 2014
PubMed
Summary

A novel tensor network, leveraging fast Fourier transform properties, efficiently represents complex many-body systems with high entanglement. This new class offers a computationally efficient alternative for studying quantum systems, including free fermions.

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Area of Science:

  • Quantum physics
  • Computational physics
  • Condensed matter theory

Background:

  • Tensor networks are crucial for simulating quantum many-body systems.
  • Representing systems with entanglement beyond the area law is computationally challenging.
  • Existing methods like the multiscale entanglement renormalization ansatz have limitations.

Purpose of the Study:

  • To introduce a new class of efficiently contractible tensor networks.
  • To demonstrate their capability in representing systems with high entanglement.
  • To provide a computationally advantageous tool for quantum system simulations.

Main Methods:

  • Utilizing the decomposability of the fast Fourier transform.
  • Developing a novel tensor network structure.
  • Applying the tensor network to translationally invariant free fermion systems and 1D systems via Jordan-Wigner transformation.

Main Results:

  • The proposed tensor network class is efficiently contractible.
  • It can represent many-body systems with local entanglement exceeding the area law.
  • Exact representation of translationally invariant free fermion systems in arbitrary dimensions and 1D systems is achieved.

Conclusions:

  • The new tensor network class provides an efficient method for simulating quantum systems.
  • It offers a promising alternative to existing methods with reduced computational demands.
  • Potential applications include variational descriptions of interacting fermion systems.