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Relation between fermionic and qubit mean fields in the electronic structure problem.

Ilya G Ryabinkin1, Scott N Genin2, Artur F Izmaylov1

  • 1Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.

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This summary is machine-generated.

Quantum computing requires transforming electronic Hamiltonians into qubit forms. Mean-field methods applied to both forms can yield different energies, depending on correlation effects and molecular orbital choices.

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Area of Science:

  • Quantum Computing
  • Computational Chemistry
  • Quantum Information Science

Background:

  • Electronic structure calculations are crucial for quantum computing.
  • Unitary transformations are used to map electronic Hamiltonians to qubit Hamiltonians.
  • Mean-field theories approximate complex many-body systems.

Purpose of the Study:

  • To investigate the differences between fermionic and qubit mean-field theories.
  • To establish conditions under which these mean-field energies are equivalent or distinct.
  • To analyze the impact of molecular orbital choice and correlation effects.

Main Methods:

  • Unitary transformation of the electronic Hamiltonian.
  • Application of mean-field procedures (e.g., Hartree-Fock) to both fermionic and qubit Hamiltonians.
  • Analysis of energy differences based on system properties.

Main Results:

  • Fermionic and qubit mean-field energies can differ significantly.
  • In low-correlation regimes, molecular orbital choice dictates energy differences.
  • In high-correlation regimes, qubit mean-field methods may exhibit symmetry breaking and yield lower energies.

Conclusions:

  • The choice of representation and correlation effects are critical when applying mean-field methods in quantum computing.
  • Understanding these differences is essential for accurate quantum simulations.
  • Further research is needed to optimize quantum algorithms for electronic structure problems.