Projection Coefficients Estimation in Continuous-Variable Quantum Circuits
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Abstract
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. This enables direct quantum estimation and visualization of the coefficient sequence -- offering a scalable, measurement-based alternative to classical numerical integration for functional analysis and non-Gaussian state characterization.