Operator commutativity screening and progressive operator block reordering toward many-body inspired quantum state...

Area of Science:

• Quantum Chemistry
• Computational Quantum Physics

Background:

• The Variational Quantum Eigensolver (VQE) is a key quantum algorithm for molecular energy calculations in the Noisy Intermediate-Scale Quantum (NISQ) era.
• Designing an expressive yet compact Ansatz is crucial for VQE accuracy and stability, but current hardware limitations pose significant challenges.
• Ansatz expressivity must balance wavefunction representation with computational efficiency to avoid numerical issues.

Purpose of the Study:

• To develop a systematic and adaptive strategy for constructing VQE Ansätze.
• To address the challenges of Ansatz expressivity, compactness, and optimization stability in quantum chemistry.
• To improve the accuracy and efficiency of molecular energy calculations using VQE.

Main Methods:

• A dynamic Ansatz construction strategy is proposed, starting with dominant operator blocks identified via commutativity screening and energy sorting.
• The Ansatz is progressively expanded through iterative operator block reordering.
• Higher-order correlation terms are incorporated using reduced lower-body tensor factorization, and adaptive construction guides optimization to mitigate local traps.

Main Results:

• The progressive operator-block addition strategy yields accurate molecular energetics with fewer parameters compared to other methods.
• The approach effectively bypasses local traps during classical optimization, enhancing stability.
• Accurate ground state energies are reproduced, even in strongly correlated systems like bond dissociation, where other methods often fail.

Conclusions:

• The proposed dynamic Ansatz construction strategy offers a robust and efficient method for VQE applications in quantum chemistry.
• This approach enhances the reliability of quantum computations for molecular systems, particularly in challenging strongly correlated regimes.
• The strategy represents a significant advancement for leveraging NISQ devices for accurate quantum chemistry calculations.