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

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.