Quantum simulation of a qubit with a non-Hermitian Hamiltonian

Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, parity-time ($\mathcal{PT}$) symmetry, and resonances. However, the quantum simulation of these models has been limited by the extensive resources necessary in iterative methods with exponentially small postselection success probability. Here we employ a fixed-depth variational circuit to circumvent these limitations, enabling simulation deep into the $\mathcal{PT}$-broken regime surrounding an exceptional point. Quantum simulations are carried out using IBM superconducting qubits. The results underscore the potential for variational quantum circuits and machine learning to push the boundaries of quantum simulation, offering new methods for exploring quantum phenomena with near-term intermediate-scale quantum technology.