  Efficiently calculating the low-lying eigenvalues of Hamiltonians, written as
sums of Pauli operators, is a fundamental challenge in quantum computing. While
various methods have been proposed to reduce the complexity of quantum circuits
for this task, there remains room for further improvement. In this article, we
introduce a new circuit design using commuting groups within the Hamiltonian to
further reduce the circuit complexity of Hamiltonian-based quantum circuits.
Our approach involves partitioning the Pauli operators into mutually commuting
clusters and finding Clifford unitaries that diagonalize each cluster. We then
design an ansatz that uses these Clifford unitaries for efficient switching
between the clusters, complemented by a layer of parameterized single qubit
rotations for each individual cluster. By conducting numerical simulations, we
demonstrate the effectiveness of our method in accurately determining the
ground state energy of different quantum chemistry Hamiltonians. Our results
highlight the applicability and potential of our approach for designing
problem-inspired ansatz for various quantum computing applications.
