Quantum-classical hybrid algorithm for the simulation of all-electron correlation

Area of Science:

• Quantum computing
• Computational chemistry
• Quantum-classical algorithms

Background:

• Quantum devices struggle with large chemical systems due to exponential scaling.
• Hybrid quantum-classical algorithms offer a path to quantum advantage by dividing computational tasks.
• Existing methods often rely on the total wave function, complicating classical post-processing.

Purpose of the Study:

• To develop a novel hybrid quantum-classical algorithm for calculating all-electron energies of strongly correlated molecules.
• To circumvent the need for the total wave function in calculations by utilizing the 2-electron reduced density matrix (2-RDM).
• To demonstrate the algorithm's accuracy and applicability on noisy intermediate-scale quantum devices.

Main Methods:

• Evaluated the 2-electron reduced density matrix (2-RDM) on a quantum device.
• Employed density matrix methods (anti-Hermitian contracted Schrödinger equation (ACSE) and multiconfiguration pair-density functional theories) on a classical computer.
• Utilized a quantum ACSE method for simulating the statically correlated 2-RDM.

Main Results:

• Successfully computed the all-electron energy of a strongly correlated molecular system.
• Achieved experimental accuracy for the relative energies of all three benzyne isomers.
• Demonstrated the algorithm's ability to yield chemically relevant and accurate results.

Conclusions:

• The developed hybrid algorithm effectively calculates molecular energies from a quantum-computed 2-RDM.
• This approach bypasses wave function dependence, enabling simpler classical post-processing.
• The method shows promise for accurate chemical simulations on current quantum hardware.