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The Quantum-Mechanical Model of an Atom02:45

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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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An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
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Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the...
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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
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Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
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A low-circuit-depth quantum computing approach to the nuclear shell model.

Chandan Sarma1, P D Stevenson1

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A new qubit mapping strategy for Variational Quantum Eigensolver (VQE) uses Slater Determinants (SD) instead of single-particle states. This simplifies quantum circuits for noisy quantum devices, showing less than 4% deviation for nuclear binding energies.

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Area of Science:

  • Nuclear Physics
  • Quantum Computing
  • Computational Chemistry

Background:

  • Variational Quantum Eigensolver (VQE) is a leading quantum algorithm for chemistry and physics simulations.
  • Current quantum hardware limitations necessitate efficient qubit mapping strategies.
  • Nuclear shell model calculations are computationally intensive.

Purpose of the Study:

  • Introduce a novel qubit mapping strategy for VQE in nuclear shell model calculations.
  • Enhance compatibility of quantum simulations with Noisy Intermediate-Scale Quantum (NISQ) devices.
  • Assess the performance of the new strategy for various nuclei.

Main Methods:

  • Developed a Slater Determinant (SD) based qubit mapping approach.
  • Applied the method to seven nuclei, including lithium isotopes, fluorine, polonium, and lead.
  • Executed ground state calculations on a noisy quantum simulator and actual quantum hardware.
  • Utilized Zero-Noise Extrapolation (ZNE) with two-qubit gate folding for error mitigation.

Main Results:

  • The SD-based mapping enables simpler quantum circuits suitable for NISQ devices.
  • Successfully simulated heavier nuclei like Polonium (22 qubits) and Lead (29 qubits).
  • Post-error mitigation, results showed less than 4% deviation from theoretical binding energies.
  • The method demonstrated particular effectiveness for lighter nuclei and two-nucleon systems.

Conclusions:

  • The proposed SD-based qubit mapping is a promising strategy for near-term quantum simulations in nuclear physics.
  • This approach offers a viable pathway for studying nuclear structure on current quantum hardware.
  • The findings pave the way for more accurate and efficient quantum simulations of atomic nuclei.