Quantum Algorithm for Imaginary-Time Green's Functions

Area of Science:

• Quantum Computing
• Computational Chemistry
• Materials Science

Background:

• Green's function methods enable accurate, improvable ab initio simulations of molecules and materials.
• Calculating the exact one-particle Green's function is computationally intensive for classical computers, limiting simulations to small systems.
• The spectral function and density of states are experimentally observable properties accessible via Green's function methods.

Purpose of the Study:

• To develop a hybrid quantum-classical algorithm for computing the imaginary-time one-particle Green's function.
• To overcome the limitations of classical computers in calculating Green's functions for larger systems.
• To provide a systematically improvable simulation method for molecular and material properties.

Main Methods:

• A hybrid quantum-classical approach combining the variational quantum eigensolver (VQE) and quantum subspace expansion (QSE).
• Calculation of the Green's function in Lehmann's representation.
• Implementation and testing on quantum simulators and IBM's quantum devices.

Main Results:

• Successful demonstration of the hybrid algorithm for calculating the imaginary-time one-particle Green's function.
• Validation of the method through simulations of H₂ and H₄ systems.
• Feasibility of the approach on current quantum hardware.

Conclusions:

• The proposed hybrid quantum-classical algorithm is a viable method for computing the one-particle Green's function.
• This approach offers a pathway to more accurate and scalable quantum simulations of molecules and materials.
• The method provides access to essential properties like spectral functions, advancing computational chemistry and materials science.