Sub-system quantum dynamics using coupled cluster downfolding techniques

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.