Hückel molecular orbital theory on a quantum computer: A scalable system-agnostic variational implementation with...

Area of Science:

• Quantum computing
• Computational chemistry
• Theoretical chemistry

Background:

• Hückel molecular orbital (HMO) theory is a semi-empirical method for analyzing conjugated π-electronic systems.
• Simulating excited states of these systems is computationally demanding on classical computers.

Purpose of the Study:

• To develop a scalable and system-agnostic quantum computing approach for HMO theory.
• To enable efficient excited state quantum simulation of conjugated π-electronic systems.

Main Methods:

• Implementation of Hückel molecular orbital (HMO) theory on a quantum computer using a variational quantum deflation (VQD) algorithm.
• Development of a compact encoding scheme for an exponential advantage in quantum simulation.
• Utilizing iterative refinement and Frobenius-inner-product-based transformations for Hamiltonian mapping.
• Formulating a symmetry-exploiting variant of VQD to mitigate error accumulation.

Main Results:

• Quantum simulation of HMO models for systems with up to 2n conjugated centers using n qubits.
• Excellent agreement between quantum simulation results (energy levels, wavefunctions) and exact classical results.
• Demonstrated successful quantum simulation of C60 fullerene using six qubits.
• Identified and addressed error accumulation in higher excited states of large systems.

Conclusions:

• The developed quantum algorithms provide a powerful tool for simulating conjugated π-electronic systems.
• The compact encoding and VQD variant offer scalability and improved accuracy for quantum simulations.
• The methodology is adaptable to diverse and complex problems across various research fields.