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Polynomial Scaling Localized Active Space Unitary Selective Coupled Cluster Singles and Doubles.

Shreya Verma1, Ruhee D'Cunha1, Abhishek Mitra1

  • 1Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States.

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A new polynomial-scaling algorithm for localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) improves quantum simulations. This method accurately predicts molecular properties, paving the way for simulating larger, chemically relevant systems.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Quantum Computing Algorithms

Background:

  • Accurate quantum chemical calculations are essential for understanding molecular behavior.
  • Coupled cluster methods, like CCSD, are highly accurate but computationally expensive.
  • Quantum computing offers potential for accelerating complex chemical simulations.

Purpose of the Study:

  • To develop a polynomial-scaling algorithm for the localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) method.
  • To enable more efficient and accurate quantum simulations of chemically relevant systems.
  • To assess the feasibility of quantum simulations for systems with large active spaces.

Main Methods:

  • Developed a polynomial-scaling algorithm for LAS-USCCSD with O(N6) memory scaling.
  • Derived gradient expressions using the generalized Wick's theorem for multireference wave functions.
  • Employed a variational quantum eigensolver on a quantum simulator to optimize cluster excitations.
  • Validated the method by calculating energy errors for polyene chains and isomerization/coupling energies for molecular systems.

Main Results:

  • Established a relationship between energy error and the amplitude selection threshold (ϵ) for polyene chains.
  • Accurately computed cis-trans isomerization energy of stilbene and magnetic coupling in a chromium dimer.
  • Estimated quantum resources for simulating a challenging (30e,22o) active space in the chromium dimer, currently beyond reach.

Conclusions:

  • The polynomial-scaling LAS-USCCSD algorithm provides an accurate and more efficient approach for quantum chemical simulations.
  • The method demonstrates practical feasibility for simulating molecular properties on quantum hardware.
  • Further development is needed to address the quantum resource demands for very large active spaces.