Quantum simulations employing connected moments expansions

Area of Science:

• Quantum Computing
• Computational Chemistry
• Condensed Matter Physics

Background:

• Advancing quantum computing (QC) requires efficient methods for many-body models.
• Current QC approaches often involve deep circuits and numerous CNOT gates, limiting scalability.
• Developing resource-efficient quantum algorithms is crucial for practical applications.

Purpose of the Study:

• To develop a novel quantum computing approach for many-body models.
• To reduce circuit depth and CNOT gate count in quantum computations.
• To enable accurate simulations of molecular and condensed matter systems.

Main Methods:

• Employed finite-order connected moment expansions (CMX) within a quantum computing framework.
• Utilized efficient procedures for initial state preparation.
• Performed classical emulations of quantum variants of CMX for benchmarking.

Main Results:

• Demonstrated the robustness and flexibility of the proposed QC approach.
• Achieved good agreement with exact solutions for the H₂ molecule potential energy surface.
• Successfully simulated the Anderson model across a wide range of correlation strengths, including dissociation and strong correlation limits.

Conclusions:

• The developed quantum computing approach effectively addresses limitations of current methods.
• The CMX-based strategy offers a viable path for accurate quantum simulations.
• This method shows promise for tackling complex problems in chemistry and physics.