Parity detection based on non-Hermitian spectral phase transition

We present a protocol for realizing parity detection of a bipartite system based on non-Hermitian spectral phase transition. The system comprises two superconducting qubits as information carriers and an auxiliary superconducting resonator. We derive a parity-dependent effective Hamiltonian, where the frequency of the resonator is shifted when the qubits are in even-parity states. The frequency shift results in a spectral phase transition in the non-Hermitian dynamical matrix in the Heisenberg picture, where the spectrum turns from purely imaginary to purely real. With a proper frequency shift, the spectral distinction between the even- and odd-parity cases leads to markedly different photon number dynamics, i.e., exponential growth for the odd-parity case, and bounded oscillations for the even-parity case. By measuring the photon number in the resonator after a fixed evolution time, the parity of the qubits can be reliably discriminated. Numerical simulations further demonstrate that the protocol is robust against systematic imperfections and decoherence, including the spontaneous emission and dephasing of the qubits, as well as cavity decay. These results establish a practical route to parity detection via non-Hermitian dynamics. This approach provides a scalable building block for superconducting-circuit quantum information processing.