Sample-efficient estimation of nonlinear quantum state functions
Estimating nonlinear functions of quantum states is essential for quantum information processing tasks such as entropy quantification, fidelity estimation, and entanglement spectroscopy. Existing approaches based on quantum state tomography incur exponential resource overhead, while methods relying on purified query access impose significant practical constraints. Here, we introduce the quantum state function framework, which extends the swap test via a linear combination of
Researchers have developed a new framework for estimating nonlinear functions of quantum states, a crucial task for applications like entropy quantification and entanglement analysis. This approach, called the quantum state function framework, improves upon existing methods that often require excessive resources or impose strict practical limitations. The new method extends the swap test using a combination of unitaries and parameterized quantum circuits. It can estimate polynomial functions of quantum states with significantly fewer copies than previous techniques, operating directly on multiple identical copies of the state.
This advancement offers a more efficient and practical way to analyze quantum data, potentially accelerating progress in quantum information processing and related fields.
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