Scalable Quantum-Classical Hybrid Algorithm for Excited States Based on Divide-and-Conquer Unitary Coupled-Cluster...

Area of Science:

• Quantum chemistry
• Computational physics
• Spectroscopy

Background:

• Excited-state simulations are crucial for understanding molecular properties.
• Current quantum methods face scalability challenges.
• Dynamical polarizability is key for extracting excitation information.

Purpose of the Study:

• Introduce a scalable quantum linear-response framework.
• Develop a divide-and-conquer approach for excited-state calculations.
• Accurately compute excitation energies and oscillator strengths.

Main Methods:

• Developed a divide-and-conquer (DC) quantum linear-response (qLR) framework.
• Utilized the variational unitary coupled-cluster ansatz with single and double excitations (qUCCSD).
• Extracted excitation energies from poles of frequency-dependent dynamical polarizability.

Main Results:

• DC-qUCCSD-LR accurately reproduces FCI excitation energies for linear hydrogen chains (nH2).
• Achieved favorable scaling: O(n^1.5) for gate counts and O(n^2.2) for measurements.
• Demonstrated reduced quantum resource requirements compared to traditional methods.

Conclusions:

• The polarizability-based qUCC-LR framework is accurate and scalable.
• The DC extension enhances computational efficiency for excited-state simulations.
• This method provides a robust foundation for future quantum simulations of molecular excitations.