Error-mitigated quantum computing of Heisenberg spin chain dynamics

We simulate the time-dependent dynamics of a three-site spin chain described by the Heisenberg XXX Hamiltonian. The quantum circuit representing the time-dependent wave function is constructed using the Suzuki-Trotter approximation, and is executed on the quantum computer ibm_kawasaki. At each time step, the density matrix of the three-qubit state is reconstructed by state tomography. By applying four different mitigation methods, Clifford data regression, Pauli twirling, density matrix purification, and density matrix orthogonalization, we demonstrate that accurate time-dependent populations and density matrices can be calculated on noisy superconducting-qubit type quantum computers.