Estimating nonlinear functions of quantum states is essential for quantum information processing but often computationally expensive. The quantum state function framework estimates a degree-n polynomial of a quantum state with \({{{\mathcal{O}}}}(n/{\varepsilon }^{2})\) copies without purified query access, enabling practical entropy, fidelity, and eigenvalue estimation.
- Hongshun Yao
- Yingjian Liu
- Xin Wang