Limitations of Hartree-Fock with quantum resources

Area of Science:

• Quantum chemistry
• Computational chemistry
• Quantum computing

Background:

• The Hartree-Fock method is a cornerstone of quantum chemistry, providing essential theoretical and computational frameworks.
• Quantum technology advancements are driving innovation in computational chemistry algorithms.
• The Hartree-Fock method is a key target for quantum-enhanced algorithms due to its central role in computational chemistry.

Purpose of the Study:

• To evaluate the suitability of quantum computing for solving the Hartree-Fock problem.
• To analyze the computational complexity of the Hartree-Fock problem in the context of quantum algorithms.
• To characterize energy landscapes for simple systems using computational methods.

Main Methods:

• Analysis of computational complexity theory, specifically non-deterministic polynomial-completeness.
• Examination of practical computational chemistry examples.
• Full characterization of energy landscapes for selected simple chemical systems.

Main Results:

• The Hartree-Fock problem is computationally complex and not a likely candidate for significant quantum speedup.
• Quantum computers and simulations present opportunities for other areas of chemistry, but not primarily for Hartree-Fock.
• Analysis reveals limitations in applying quantum enhancement to this specific computational chemistry problem.

Conclusions:

• The Hartree-Fock problem's computational complexity makes it an unlikely candidate for quantum computing enhancement.
• While quantum computing holds promise for computational chemistry, its application to Hartree-Fock is limited.
• Further research should focus on quantum algorithms for problems better suited to quantum computational advantages.