Rayleigh-Ritz calculations in Segal-Bargmann space recover the exact harmonic-oscillator ground state and yield perturbative energy expansions for the quartic anharmonic oscillator via adaptive Gaussian trial functions.
Bargmann,On a Hilbert space of analytic functions and an associated integral transform part I, Commun
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A CV quantum circuit protocol prepares the state |f> for a holomorphic function f(z) and estimates coefficients c_n = <n|f> via photon-number-resolved detection with interferometric phase referencing.
Quantum gates are realized as differential operators on holomorphic functions that preserve the qubit subspace and act as canonical transformations on a toroidal geometry.
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Rayleigh-Ritz Variational Method in The Complex Plane
Rayleigh-Ritz calculations in Segal-Bargmann space recover the exact harmonic-oscillator ground state and yield perturbative energy expansions for the quartic anharmonic oscillator via adaptive Gaussian trial functions.
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Geometry of Quantum Logic Gates
Quantum gates are realized as differential operators on holomorphic functions that preserve the qubit subspace and act as canonical transformations on a toroidal geometry.