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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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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
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Hamiltonian simulation-based quantum-selected configuration interaction for large-scale electronic structure

Kenji Sugisaki1,2,3,4, Shu Kanno1,5, Toshinari Itoko1,6

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Summary
This summary is machine-generated.

Hamiltonian simulation-based QSCI (HSB-QSCI) offers a new quantum chemistry method. It efficiently calculates molecular energies by sampling Slater determinants from quantum states, improving accuracy for challenging systems.

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Area of Science:

  • Quantum chemistry
  • Computational physics
  • Quantum computing applications

Background:

  • Conventional Quantum-Selected Configuration Interaction (QSCI) relies on preparing high-quality wave functions for accurate quantum chemical calculations.
  • This preparation step is a bottleneck, especially for strongly correlated systems.

Purpose of the Study:

  • To introduce a novel Hamiltonian simulation-based QSCI (HSB-QSCI) method.
  • To overcome the limitations of traditional QSCI by avoiding the need for explicit high-quality approximate wave function preparation.

Main Methods:

  • HSB-QSCI samples Slater determinants from quantum states generated via real-time evolution of approximate wave functions.
  • Numerical simulations were performed for oligoacenes, phenylene-1,4-dinitrene, and hexa-1,2,3,4,5-pentaene.
  • Hardware demonstrations were conducted on an IBM quantum processor for carbyne molecules up to 36 qubits.

Main Results:

  • HSB-QSCI successfully calculates energies for both simple and strongly correlated systems.
  • The method captured over 99.18% of correlation energies using only ~1% of Slater determinants in 36-qubit systems.
  • Demonstrated applicability to molecules requiring significant quantum resources.

Conclusions:

  • HSB-QSCI is a robust and efficient method for quantum chemical calculations on current quantum computers.
  • The approach significantly reduces the computational burden by efficiently selecting relevant electronic configurations.
  • HSB-QSCI shows promise for advancing quantum computing applications in chemistry.