Critical Limitations in Quantum-Selected Configuration Interaction Methods.

Area of Science:

• Quantum computing
• Computational chemistry
• Quantum algorithms

Background:

• Quantum Selected Configuration Interaction (QSCI), also known as Sample-based Quantum Diagonalization (SQD), is a near-term quantum computing approach for the electronic Schrödinger equation.
• Classical Selected Configuration Interaction (SCI) heuristics are established methods for solving electronic structure problems.

Purpose of the Study:

• To perform a numerical analysis of Quantum Selected Configuration Interaction (QSCI) methods.
• To identify and demonstrate critical limitations hindering the practical applicability of QSCI in chemistry.

Main Methods:

• Numerical analysis using nitrogen molecules and [2Fe-2S] iron-sulfur clusters.
• Comparison of QSCI determinant sampling with classical SCI heuristics.
• Evaluation of CI expansion compactness and accuracy.

Main Results:

• QSCI methods exhibit inefficiencies in discovering new determinants due to repeated sampling of existing configurations.
• These inefficiencies are exacerbated when pursuing high accuracy or sampling from approximate ansatze.
• When sampling issues are absent, QSCI yields less compact CI expansions than classical methods, increasing computational cost.
• A fundamental trade-off exists between determinant quantity and CI expansion compactness/accuracy in QSCI.

Conclusions:

• QSCI methods face significant practical limitations in quantum chemistry applications.
• The inherent inefficiencies and less compact expansions make QSCI less competitive than classical SCI heuristics.
• Further development is needed to overcome these drawbacks for viable quantum chemistry computations.