Adaptive Variational Quantum Computing Approaches for Green's Functions and Nonlinear Susceptibilities

Area of Science:

• Quantum computing
• Computational physics
• Quantum chemistry

Background:

• Calculating real-time single-particle Green's functions and nonlinear susceptibilities is crucial for understanding Hamiltonian systems.
• Traditional methods face challenges with complex quantum systems, necessitating novel computational approaches.

Purpose of the Study:

• To present and benchmark quantum computing approaches for calculating real-time Green's functions and nonlinear susceptibilities.
• To demonstrate the feasibility of these methods on near-term quantum processors.

Main Methods:

• Leveraging adaptive variational quantum algorithms for state preparation and propagation.
• Utilizing automatically generated compact circuits for dynamical evolution.
• Employing statevector simulators on classical hardware for benchmarking.

Main Results:

• Accurate Green's function calculations for Fermi-Hubbard chains (4 and 6 sites) and the LiH molecule.
• Successful calculation of third-order nonlinear susceptibilities for a quantum spin-1 model with Dzyaloshinskii-Moriya interaction.
• Demonstrated feasibility with varying ansatz circuit depths.

Conclusions:

• Real-time quantum computing approaches using adaptive parametrized circuits are viable for evaluating linear and nonlinear response functions.
• These methods show potential for application with near-term quantum processors.
• The study provides a pathway for quantum simulations in condensed matter and molecular systems.