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Related Concept Videos

Quantum Numbers02:43

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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Universal quantum Hamiltonians.

Toby S Cubitt1, Ashley Montanaro2, Stephen Piddock2

  • 1Department of Computer Science, University College London, London WC1E 6BT, United Kingdom; t.cubitt@ucl.ac.uk.

Proceedings of the National Academy of Sciences of the United States of America
|September 1, 2018
PubMed
Summary
This summary is machine-generated.

Simple spin-lattice models can simulate the complex physics of any quantum many-body system. This research proves universality in quantum simulation, potentially reducing the need for error correction in quantum technologies.

Keywords:
Hamiltonian complexitymany-body physicsquantum information theoryquantum simulation

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Quantum Simulation

Background:

  • Quantum many-body systems display a vast array of complex phases and phenomena.
  • Understanding and simulating these systems is crucial for advancing physics and technology.
  • Analogue quantum simulation offers a practical approach to studying these systems.

Purpose of the Study:

  • To rigorously define and prove the universality of certain spin-lattice models for quantum simulation.
  • To classify the simulation capabilities of all two-qubit interactions.
  • To establish a theoretical foundation for analogue Hamiltonian simulation.

Main Methods:

  • Formal characterization of quantum system simulation.
  • Exhaustive classification of the simulation power of two-qubit interactions.
  • Theoretical analysis of spin-lattice models.

Main Results:

  • Demonstrated that specific, simple spin-lattice models are universal simulators.
  • Proved that these universal models can replicate the entire physics of any quantum many-body system.
  • Fully classified the simulation power inherent in all two-qubit interactions.

Conclusions:

  • Established the universality of certain spin-lattice models, providing a rigorous basis for analogue Hamiltonian simulation.
  • These findings suggest that complex quantum systems can be simulated using simpler, universal models.
  • The results may alleviate the necessity of quantum error correction for certain quantum information technologies.