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

Abstract

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 the presence of 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, as well as 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 of the ground-state energy and fidelity improves substantially by increasing the number of layers used in the ansatzes. From the cloud experiments, we find that the ground-state energies extracted from realizations across different quantum computers and system sizes reach the expected values to within errors that are small (i.e., on the percent level), including the inference of the energy density in the thermodynamic limit from these values. We achieve this accuracy through a combination of physics-motivated variational ansatzes, and efficient, scalable energy-measurement and error-mitigation protocols, including the use of a reference state in the zero-noise extrapolation. By using a 102-qubit system, we have been able to successfully apply 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 that a standalone hybrid quantum-classical variational approach for large-scale $XXZ$ models considered in this work is feasible.