  Achieving chemical accuracy with shallow quantum circuits is a significant
challenge in quantum computational chemistry, particularly for near-term
quantum devices. In this work, we present a Clifford-based Hamiltonian
engineering algorithm, namely CHEM, that addresses the trade-off between
circuit depth and accuracy. Based on variational quantum eigensolver and
hardware-efficient ansatz, our method designs Clifford-based Hamiltonian
transformation that (1) ensures a set of initial circuit parameters
corresponding to the Hartree--Fock energy can be generated, (2) effectively
maximizes the initial energy gradient with respect to circuit parameters, (3)
imposes negligible overhead for classical processing and does not require
additional quantum resources, and (4) is compatible with any circuit topology.
We demonstrate the efficacy of our approach using a quantum hardware emulator,
achieving chemical accuracy for systems as large as 12 qubits with fewer than
30 two-qubit gates. Our Clifford-based Hamiltonian engineering approach offers
a promising avenue for practical quantum computational chemistry on near-term
quantum devices.
