Practical quantum simulation of small-scale non-Hermitian dynamics

Non-Hermitian quantum systems have recently attracted considerable attention due to their exotic properties. Though many experimental realizations of non-Hermitian been reported, the non-Hermiticity usually resorts hard-to-control environments and cannot last for too long times. An alternative approach is use simulation with closed system, whereas how simulate Hamiltonian dynamics remains a great challenge. To tackle this problem, we propose protocol which combines dilation method variational algorithm. The used transform into Hermitian one through an exquisite circuit, while algorithm efficiently approximating complex entangled gates in circuit. As demonstration, apply our Ising chain nonlocal perturbations, important model study phase transition at nonzero temperatures. numerical results are highly consistent theoretical predictions, revealing effectiveness protocol. presented paves way practically simulating small-scale dynamics.