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Dynamical structure factors of dynamical quantum simulators.

Maria Laura Baez1,2, Marcel Goihl2, Jonas Haferkamp2

  • 1Condensed Matter Division, Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany; baez@pks.mpg.de.

Proceedings of the National Academy of Sciences of the United States of America
|October 3, 2020
PubMed
Summary
This summary is machine-generated.

Calculating dynamical structure factors for strongly correlated systems is computationally hard. This study shows quantum simulators can overcome these classical limitations, even with noisy near-term devices.

Keywords:
Rydberg atomsdynamical structure factorquantum simulationtrapped ions

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Science
  • Computational Physics

Background:

  • Dynamical structure factors are crucial for validating microscopic descriptions of strongly correlated systems.
  • Numerical calculation of dynamical structure factors is challenging due to inherent approximations.
  • Classical tracking of time evolution under local Hamiltonians is computationally intensive.

Purpose of the Study:

  • To investigate the computational hardness of dynamical structure factors in relation to classical simulation limitations.
  • To explore the potential of quantum simulators for calculating these factors.
  • To propose an improved measurement setup for determining dynamical structure factors.

Main Methods:

  • Analysis of the inheritance of computational hardness from time evolution tracking to dynamical structure factors.
  • Theoretical argument for the bounded-error quantum polynomial time ([Formula: see text])-hardness of accessible dynamical structure factors.
  • Development and description of a novel measurement setup applicable to various quantum computing architectures.

Main Results:

  • Practically accessible dynamical structure factors are shown to be ([Formula: see text])-hard for general local Hamiltonians.
  • A novel measurement setup is presented for determining dynamical structure factors across diverse quantum platforms (cold atoms, trapped ions, Rydberg atoms, superconducting qubits).
  • Quantum simulations on near-term noisy devices can observe dynamical structure factors for larger system sizes than classical simulations.

Conclusions:

  • The computational complexity of dynamical structure factors aligns with the capabilities of quantum simulators.
  • The proposed measurement setup facilitates experimental determination of dynamical structure factors.
  • Near-term quantum devices offer a viable path for studying quantum matter via dynamical structure factors, surpassing classical limitations.