Energy Landscapes for the Unitary Coupled Cluster Ansatz

Area of Science:

• Quantum Computing
• Computational Chemistry
• Quantum Algorithms

Background:

• The Unitary Coupled Cluster (UCC) approach is a popular wavefunction parametrization for variational quantum eigensolvers.
• It offers advantages in optimization compared to hardware-efficient ansätze.
• Understanding the UCC energy landscape is crucial for its application in quantum algorithms.

Purpose of the Study:

• To explore the energy landscape of the Unitary Coupled Cluster Singles and Doubles (UCCSD) wavefunction.
• To investigate how the solution space organization changes with UCC ansatz variations.
• To identify challenges in finding the global minimum energy for UCCSD.

Main Methods:

• Investigated the energy landscape of UCCSD for lithium hydride and nitrogen dimer systems.
• Analyzed the organization of the solution space, focusing on local minima.
• Varied the number and order of operators in the UCC ansatz.

Main Results:

• UCCSD energy landscapes consistently show numerous low-lying minima.
• High energy transition states connect these numerous minima.
• The energy spread of minima near the global minimum can exceed chemical accuracy.

Conclusions:

• The complex energy landscape of UCCSD presents significant challenges for locating the global minimum.
• Variations in ansatz structure impact the organization of the solution space.
• Further research is needed to develop strategies for navigating these challenging energy landscapes in quantum computing applications.