Generalized Unitary Coupled Cluster Wave functions for Quantum Computation.

Area of Science:

• Quantum Computing
• Computational Chemistry
• Quantum Algorithms

Background:

• Unitary coupled-cluster (UCC) ansätze are crucial for quantum chemistry simulations.
• Existing methods like UCCGSD and UCCSD face challenges in terms of computational cost and scalability on near-term quantum devices.

Purpose of the Study:

• Introduce a novel, efficient, and systematically improvable UCC ansatz, k-UpCCGSD, for quantum computing.
• Compare the performance (accuracy and implementation efficiency) of k-UpCCGSD against UCCGSD and UCCSD.
• Evaluate the accuracy of these methods for both ground and excited states of molecular systems.

Main Methods:

• Developed k-UpCCGSD, utilizing sparse generalized doubles operators and k products of pair coupled-cluster double excitations (pCCD) with generalized singles.
• Performed classical benchmark calculations for H4, H2O, and N2 ground and excited states.
• Employed an orthogonally constrained variational quantum eigensolver for excited state calculations.

Main Results:

• k-UpCCGSD demonstrates superior scaling for quantum computing, requiring lower circuit depth compared to UCCGSD and UCCSD.
• k-UpCCGSD achieves chemical accuracy for ground states with a favorable balance of accuracy and cost.
• UCCGSD is more accurate than UCCSD but computationally more expensive.
• Excited state calculations using variational methods showed reduced accuracy, which was improved by using specialized multideterminantal reference states.

Conclusions:

• k-UpCCGSD presents a promising, cost-effective, and accurate alternative for quantum chemistry on near-term quantum computers.
• The study highlights the trade-offs between accuracy and computational cost for different UCC ansätze.
• Improvements in excited state calculations can be achieved through advanced reference state constructions.