Enhancing quantum utility: simulating large-scale quantum spin chains on superconducting quantum computers

Abstract: 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.