Enhancing quantum utility: simulating large-scale quantum spin chains on
  superconducting quantum computers
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.
Talal Ahmed Chowdhury Kwangmin Yu Mahmud Ashraf Shamim M. L. Kabir Raza Sabbir Sufian