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In quantum physics, observables are generally believed to be Hermitian, but there are several examples of non-Hermitian systems possessing real positive eigenvalues, particularly among open systems. Here, the authors simulate the evolution of a non-Hermitian Hamiltonian on a superconducting quantum processor using a dilation procedure involving an ancillary qubit, and observe the parity–time (PT)-symmetry breaking phase transition at the exceptional points.