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.

我们模拟了由海森堡XXX哈密顿量描述的三格点自旋链的含时动力学。代表含时波函数的量子电路是使用铃木 - 特罗特近似构建的，并在量子计算机ibm_kawasaki上执行。在每个时间步长，通过态层析成像重建三量子比特态的密度矩阵。通过应用四种不同的缓解方法，克利福德数据回归、泡利旋转、密度矩阵纯化和密度矩阵正交化，我们证明了在有噪声的超导量子比特类型的量子计算机上可以计算出准确的含时布居数和密度矩阵。