  We devise quantum circuit implementation of exponential of scaled $n$-qubit
Pauli-strings using one-qubit rotation gates and CNOT gates. These circuits can
be implemented in low-connected quantum hardware, in particular, star graph
architecture for digital quantum computation. Then these circuits are employed
to simulate classes of 1D Hamiltonian operators that include $2$-sparse
Hamiltonian, Ising Hamiltonian, and both time-independent and time-dependent
Random Field Heisenberg Hamiltonian and Transverse Magnetic Random Quantum
Ising Hamiltonian by approximating its unitary evolution with first-order
Suzuki-Trotter expansion. Finally, we perform noisy Hamiltonian simulation of
these circuits using different noise models to investigate Hamiltonian
simulation on NISQ devices.
