Engineering non-Gaussian bosonic gate through quantum signal processing

Non-Gaussian operations are essential for most bosonic quantum technologies. Yet, realizable non-Gaussian operations are rather limited in type and generally suffer from accuracy-duration tradeoffs. In this work, we propose to use quantum signal processing techniques to engineer non-Gaussian operations in hybrid qubit-oscillator systems. For systems with dispersive coupling, our scheme can generate a new non-Gaussian gate that produces a phase shift depending on the modulus of boson number. This gate reproduces the selective number-dependent arbitrary phase (SNAP) and exponential-parity gates under certain parameter choices, and high accuracy can be achieved within a short, fixed, excitation-independent interaction time. The gate can be used for a variety of tasks, e.g. entangling logical qudits and deterministically generating multi-component cat states. Additionally, our versatile QSP formalism can be extended to systems with other interactions, such as Jaynes-Cummings interaction, and engineer non-unitary operations, such as generalized-parity measurement and noiseless linear amplification.