A kinetic-energy augmented VQE for high-fidelity, shallow-depth state preparation

We present Variational Hamiltonian Descent (VHD), a VQE variant that augments a shallow ansatz with a decaying kinetic-energy–like drive, achieving higher fidelities and faster convergence at substantially lower depth than standard problem-specific and hardware-efficient baselines. Motivated by Quantum Hamiltonian Descent, we develop a variational, hardware-aware formulation in which the kinetic drive encourages early exploration and then tapers to enable convergence. We benchmark our proposed VHD algorithm on the critical transverse-field Ising model (TFIM) with numerical simulations up to 30 qubits. Across system sizes, we observe consistent relative gains: at fixed circuit depth, VHD yields at least 2× larger fidelities than standard VQE with reduced run-to-run variability. For a fixed target fidelity, VHD reaches the goal with several-fold fewer native gates and much shallower circuits. These results indicate that including a kinetic drive in VQE provides a practical path to high-fidelity ground-state preparation on NISQ hardware and we are currently preparing validation experiments on IBM's Heron processors.