Simulating large-size quantum spin chains on cloud-based superconducting quantum computers

Quantum computers have the potential to efficiently simulate large-scale quantum systems for which classical approaches are bound to fail. Even though several existing quantum devices now feature total qubit numbers of more than 100, their applicability remains plagued by noise and errors. Thus, the degree to which large quantum systems can successfully be simulated on these devices remains unclear. Here, we report on numerical results of physics-motivated variational ansatzes and cloud simulations performed on several of IBM's superconducting quantum computers to simulate ground states of spin chains having a wide range of system sizes up to 102 qubits. Our numerical analysis shows that the accuracy and fidelity of the ground-state energy improve substantially by increasing the number of layers used in the ansatzes. The cloud experiments show that the ground-state energies extracted from realizations across different quantum computers and system sizes reach the expected values to within errors on the percent level, including the inference of the energy density in the thermodynamic limit. We achieve this accuracy through a combination of physics-motivated variational ansatzes and efficient, scalable energy-measurement and error-mitigation protocols, including using a reference state in the zero-noise extrapolation. Using a 102-qubit system, we have successfully applied up to 3186 CNOT gates in a single circuit when performing gate-error mitigation. Our accurate, error-mitigated results for random parameters in the ansatz states suggest a standalone hybrid quantum-classical variational approach for large-scale XXZ models considered in this work is feasible.