Wave Function Adapted Hamiltonians for Quantum Computing.

Area of Science:

• Quantum Computing
• Quantum Chemistry
• Computational Physics

Background:

• Noisy Intermediate-Scale Quantum (NISQ) devices show promise for quantum chemistry applications like the Variational Quantum Eigensolver (VQE).
• A key challenge for VQE is designing compact, shallow quantum circuit ansatzes that capture the complexity of electronic structures.
• Existing VQE methods often struggle with limited variational flexibility and susceptibility to local minima.

Purpose of the Study:

• To develop a modified VQE scheme that overcomes limitations in circuit ansatz design for quantum chemistry.
• To introduce a method that adapts the molecular Hamiltonian to the circuit ansatz, improving accuracy and reducing dependence on circuit topology.
• To enhance the ability of quantum algorithms to recover electron correlation with shallow quantum circuits.

Main Methods:

• Introduced a novel method named Wavefunction Adapted Hamiltonian Through Orbital Rotation (WAHTOR).
• Adapted the molecular Hamiltonian to the circuit ansatz via an optimization procedure.
• Utilized molecular orbital rotations to optimize the Hamiltonian, calculating gradients efficiently without significant computational overhead.

Main Results:

• Numerical simulations on small molecules demonstrated that WAHTOR is less dependent on circuit topology compared to standard VQE.
• The method showed reduced susceptibility to high-energy local minima, a common issue in VQE.
• WAHTOR successfully recovered significant electron correlation even with simple, shallow-depth empirical ansatzes.

Conclusions:

• The WAHTOR method offers a robust and feasible approach for quantum chemistry on NISQ devices.
• It enhances the accuracy and efficiency of VQE by adapting the Hamiltonian, mitigating limitations of fixed ansatzes.
• Further research should focus on the hardware requirements for applying WAHTOR on future NISQ hardware.