Self-consistent Quantum Linear Response with a Polarizable Embedding Environment.

Quantum computing presents a promising avenue for solving complex problems, particularly in quantum chemistry, where it could accelerate the computation of molecular properties and excited states. This work focuses on computing excitation energies with hybrid quantum-classical algorithms for near-term quantum devices, combining the quantum linear response (qLR) method with a polarizable embedding (PE) environment. We employ the self-consistent operator manifold of quantum linear response (q-sc-LR) on top of a unitary coupled cluster (UCC) wave function in combination with a Davidson solver. The latter removes the need to construct the entire electronic Hessian, improving computational efficiency when going toward larger molecules. We introduce a new superposition-state-based technique to compute Hessian-vector products and show that this approach is more resilient toward noise than our earlier gradient-based approach. We demonstrate the performance of the PE-UCCSD model on systems such as butadiene and para-nitroaniline in water and find that PE-UCCSD delivers comparable accuracy to classical PE-CCSD methods on such simple closed-shell systems. We also explore the challenges posed by hardware noise and propose simple error mitigation techniques to maintain accurate results on noisy quantum computers.