Transcorrelated Hamiltonians for Error-Resilient Quantum Simulations

McArdle et al. (2020) showed transcorrelated methods reduce quantum resources by embedding electron correlation into a transformed Hamiltonian, but non-Hermiticity complicates quantum implementation. This idea proposes error-mitigated quantum algorithms tailored for non-Hermitian operators: e.g., using imaginary-time evolution with subspace expansion or variational quantum deflation. It extends Shen et al.’s UCC work by replacing the baseline Hamiltonian with a transcorrelated version, slashing circuit depth. For TiH (Clary et al. 2022), this could make d-orbital simulations feasible on near-term devices by reducing gate counts below error thresholds. The novelty lies in co-designing the transcorrelated transformation with noise-aware quantum protocols.

References:

1. Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure. Yangchao Shen, Xiang Zhang, Shuaining Zhang, Jing-Ning Zhang, M. Yung, Kihwan Kim (2015).
2. Exploring the scaling limitations of the variational quantum eigensolver with the bond dissociation of hydride diatomic molecules. Jacob M. Clary, E. Jones, Derek Vigil-Fowler, Christopher Chang, P. Graf (2022). International Journal of Quantum Chemistry.
3. Improving the accuracy of quantum computational chemistry using the transcorrelated method. Sam McArdle, D. Tew (2020).