Projection Coefficients Estimation in Continuous-Variable Quantum Circuits
This work provides a hardware-native quantum protocol for analyzing functions defined by quantum oracles, complementing classical numerical integration in quantum information processing.
The paper proposes a continuous-variable quantum algorithm to compute projection coefficients of holomorphic functions in the Segal-Bargmann space, using photon-number-resolved detection and interferometric phase referencing to recover complex amplitudes. The protocol is analyzed under realistic noise models, enabling direct estimation of coefficient sequences for non-Gaussian state characterization.
In this work, we propose a continuous-variable quantum algorithm to compute the projection coefficients of a holomorphic function in the Segal--Bargmann space by leveraging its isometric correspondence with single-mode quantum states. Using CV quantum circuits, we prepare the state $\ket{f}$ associated with $f(z)$ and extract the coefficients $c_n = \braket{n}{f}$ via photon-number-resolved detection, enhanced by interferometric phase referencing to recover full complex amplitudes. We detail the construction of the state-preparation oracle for various functional classes and analyze the protocol's robustness under realistic noise models, including detector inefficiency and state preparation errors. This enables direct quantum estimation and visualization of the coefficient sequence -- offering a hardware-native protocol for characterizing non-Gaussian states and analyzing functions defined by quantum oracles, complementary to classical numerical integration.