  We present the quantum simulation of the frustrated quantum
spin-$\frac{1}{2}$ antiferromagnetic Heisenberg spin chain with competing
nearest-neighbor $(J_1)$ and next-nearest-neighbor $(J_2)$ exchange
interactions in the real superconducting quantum computer with qubits ranging
up to 100. In particular, we implement, for the first time, the Hamiltonian
with the next-nearest neighbor exchange interaction in conjunction with the
nearest neighbor interaction on IBM's superconducting quantum computer and
carry out the time evolution of the spin chain by employing first-order
Trotterization. Furthermore, our novel implementation of second-order
Trotterization for the isotropic Heisenberg spin chain, involving only
nearest-neighbor exchange interaction, enables precise measurement of the
expectation values of staggered magnetization observable across a range of up
to 100 qubits. Notably, in both cases, our approach results in a constant
circuit depth in each Trotter step, independent of the initial number of
qubits. Our demonstration of the accurate measurement of expectation values for
the large-scale quantum system using superconducting quantum computers
designates the quantum utility of these devices for investigating various
properties of many-body quantum systems. This will be a stepping stone to
achieving the quantum advantage over classical ones in simulating quantum
systems before the fault tolerance quantum era.
