Quantum Computing of a Frenkel Hamiltonian with Deep Learning-Based Error Mitigation*

In recent decades, the development of quantum computers and quantum algorithms has made significantly progress in the physics and chemistry communities. Among various studied systems, one notable system that has not been simulated by quantum computers is the Frenkel-Davydov (FD) Hamiltonian, typically used to model the excitonic effects in organic solids. In this study, we used a single layer anthracene as a toy model and employed variational quantum deflation (VQD) to compute all the eigenvalues and associated observables. To address errors introduced by noisy qubits, we developed a novel error mitigation framework that incorporates post-selection (PS) gates and a deep learning (DL) technique to obtain the mitigated expectation value. We first demonstrate excellent agreement between the eigenvalues calculated on a noiseless simulator and those obtained through exact diagonalization, confirming the validity of our VQD algorithm. Furthermore, we have observed the effective mitigation of noisy results using our PS+DL technique for systems with more than 8 qubits on a noisy simulator. Remarkably, this technique remains effective for real hardware, even when calibrations occur during the simulations. Our results promise to contribute to the development of excited state discovery and new mitigation techniques within the quantum computing community.