Noisy normal arbitrary quantum superposition state reconstruction based on parameterized quantum circuits

To efficiently reconstruct noisy quantum states, specifically the normal arbitrary superposition state (NASS), on a quantum computer, we propose a reconstruction scheme based on parameterized quantum circuits (PQCs). First, the NASS image representation method is adopted, encoding images as quantum states, and a PQC is designed for reconstructing NASS. Then, gradient descent is used to train and update the circuit parameters. Finally, experiments validate the reconstruction of the quantum state. Experimental results show that for noisy grayscale image reconstruction, the structural similarity index measure reaches 0.922, and the peak signal-to-noise ratio is 26.74 dB. In terms of algorithmic complexity, the proposed scheme has a complexity of 4n2−4n+1, requiring no ancillary qubits. The proposed reconstruction scheme for noisy NASS quantum states offers the advantages of requiring fewer qubits and lower complexity while achieving effective reconstruction performance.