Fast gradient-free optimization of excitations in variational quantum eigensolvers.

Area of Science:

• Quantum computing
• Computational chemistry
• Quantum algorithms

Background:

• Variational quantum eigensolvers (VQEs) are key for quantum chemistry.
• Current optimizers struggle with complex excitation operators used in physically motivated ansätze.
• Existing methods like Rotosolve are limited to simpler operator types.

Purpose of the Study:

• Introduce ExcitationSolve, a novel quantum-aware optimizer.
• Extend optimization capabilities to parameterized unitaries with specific generator properties (G^3 = G).
• Enable efficient optimization for excitation operators in quantum chemistry.

Main Methods:

• ExcitationSolve is a globally-informed, gradient-free, and hyperparameter-free optimizer.
• It determines global optima per parameter using quantum resources equivalent to one gradient-based update step.
• Strategies for fixed and adaptive ansätze, including simultaneous multi-excitation optimization, are provided.

Main Results:

• ExcitationSolve outperforms state-of-the-art optimizers on molecular ground state energy benchmarks.
• Achieves chemical accuracy for equilibrium geometries rapidly (single parameter sweep).
• Yields shallower adaptive ansätze and demonstrates robustness against hardware noise.

Conclusions:

• ExcitationSolve offers a significant advancement for quantum chemistry on quantum computers.
• Unites physical insight with efficient optimization for scalable calculations.
• Paves the way for more accurate and efficient molecular simulations.