Reducing Circuit Depth in Adaptive Variational Quantum Algorithms via Effective Hamiltonian Theories

Area of Science:

• Quantum computing
• Computational chemistry
• Electronic structure theory

Background:

• Quantum computers are promising for electronic structure calculations.
• Current quantum devices struggle with the complex quantum circuits needed for highly entangled wave functions in variational quantum eigensolver (VQE) algorithms.
• Adapting VQE for near-term hardware requires reducing circuit complexity.

Purpose of the Study:

• To develop a new scheme for constructing effective Hamiltonians.
• To adapt VQE algorithms for current quantum hardware limitations.
• To enable accurate electronic structure calculations with shallower quantum circuits.

Main Methods:

• Proposed a novel method to construct an effective Hamiltonian using a product of linear combinations of excitation operators.
• Integrated this effective Hamiltonian into adaptive VQE algorithms.
• Performed numerical simulations for small molecules using the new scheme.

Main Results:

• The new scheme results in a quadratic multiplicative growth of the effective Hamiltonian.
• Maintained constant-size quantum circuits within the adaptive VQE framework.
• Achieved milli-Hartree accuracy in a minimal basis for small molecules.
• Demonstrated significantly shallower circuit depths compared to standard methods.

Conclusions:

• The proposed effective Hamiltonian method is a viable approach for adapting VQE to near-term quantum hardware.
• This method significantly reduces the resource requirements for electronic structure calculations.
• Enables more accurate and efficient quantum simulations of molecular systems.