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This study extends coupled cluster methods to the time domain, enabling accurate quantum dynamics simulations for larger systems. The developed time-dependent formalism allows partitioning systems for efficient computation and novel quantum algorithm development.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Theoretical Chemistry

Background:

  • Coupled cluster (CC) methods are powerful tools for electronic structure calculations.
  • The double unitary coupled cluster (DUCC) ansatz offers an exact representation of the many-body wave function.
  • Extending CC formalisms to the time domain is crucial for simulating quantum dynamics.

Purpose of the Study:

  • To extend the sub-system embedding sub-algebra coupled cluster formalism and the DUCC ansatz to the time domain.
  • To demonstrate the exactness of the DUCC ansatz for time-dependent problems.
  • To develop a formalism for partitioning quantum systems into slowly and rapidly varying sub-systems.

Main Methods:

  • Extension of the coupled cluster formalism to the time-dependent Schrödinger equation.
  • Mathematical proof of the exactness of the DUCC ansatz for anti-Hermitian cluster operators.
  • Development of downfolded/effective Hamiltonians for active spaces.
  • Application of the quantum Lanczos approach.

Main Results:

  • The DUCC ansatz is proven to be exact in the time domain.
  • A method is established to partition quantum systems into time-dependent sub-systems.
  • Downfolded Hamiltonians effectively remove irrelevant fermionic degrees of freedom.
  • The time-dependent formalism enables quantum dynamics simulations for larger systems.

Conclusions:

  • The developed time-dependent coupled cluster formalism accurately describes quantum dynamics.
  • This approach facilitates the simulation of larger quantum systems.
  • Novel quantum algorithms can be formulated using this time-dependent framework, including the quantum Lanczos approach.