Thermal Weight Determination and Interstate Coupling in State-Averaged ADAPT-VQE.

Area of Science:

• Quantum computing
• Quantum chemistry
• Condensed matter physics

Background:

• Characterizing low-temperature electronic thermal states is crucial but challenging.
• Variational Quantum Eigensolver (VQE) methods, like ADAPT-VQE, are successful for quantum state preparation.
• Existing methods can be generalized for excited and Gibbs states.

Purpose of the Study:

• Introduce Helmholtz-Optimized Thermal (HOT) ADAPT-VQE, an ancilla-free strategy.
• Prepare Gibbs states by directly minimizing Helmholtz free energy.
• Target dominant eigenstates of thermal ensembles.

Main Methods:

• Developed HOT ADAPT-VQE, a novel quantum algorithm.
• Applied the method to two model systems: Fe2+ cation and a [Cu2O7]10- fragment.
• Compared HOT ADAPT-VQE with existing multistate ADAPT-VQE variants.

Main Results:

• HOT ADAPT-VQE accurately predicts free energy for systems with strongly correlated ground states.
• Achieved significant improvements over previous Gibbs-state estimation methods.
• Demonstrated shallower quantum circuits compared to existing approaches.

Conclusions:

• HOT ADAPT-VQE is a promising method for thermal state calculations.
• The ancilla-free strategy offers efficiency gains in quantum computing.
• Advances the application of quantum computing in chemistry and physics.