Graph-|Q⟩⟨C|, a Graph-Based Quantum/Classical Algorithm for Efficient Electronic Structure on Hybrid...

Area of Science:

• Quantum Computing
• Computational Chemistry
• Electronic Structure Theory

Background:

• Accurate computation of post-Hartree-Fock electronic structure energies is crucial for understanding molecular behavior.
• Scaling quantum algorithms to large molecular systems remains a significant challenge due to resource limitations.

Purpose of the Study:

• To develop a novel procedure for reducing quantum circuit depth and enhancing accuracy in electronic structure calculations.
• To enable efficient computation on hybrid quantum-classical hardware ensembles.

Main Methods:

• A graph-theoretic molecular fragmentation technique is employed to divide large systems into smaller, manageable overlapping fragments.
• Projection operators are utilized to decompose unitary evolution, allowing parallel processing on quantum and classical hardware.
• The methodology was demonstrated by computing Unitary Coupled Cluster Singles and Doubles (UCCSD) energies for hydrogen clusters ([H2]n).

Main Results:

• The developed procedure significantly reduces quantum circuit depth and the number of CNOT gates, achieving up to a 9-order of magnitude improvement compared to standard Qiskit implementations.
• Accurate UCCSD energies were obtained for [H2]n clusters (n=4-128) using quantum simulators, with results in the milli-hartree energy range.
• The asynchronous spawning of electronic structure computations onto hybrid hardware ensembles was successfully demonstrated.

Conclusions:

• The proposed molecular fragmentation and circuit decomposition method offers a scalable and efficient approach for quantum electronic structure calculations.
• This technique substantially reduces the computational resources required, paving the way for tackling larger and more complex molecular systems.
• The hybrid quantum-classical approach enhances the feasibility of applying quantum computing to real-world chemical problems.