# Engineering Non-Gaussian Bosonic Gates through Quantum Signal Processing

## TL;DR

This paper introduces a quantum signal processing method to engineer high-accuracy non-Gaussian bosonic gates on hybrid systems, enabling advanced quantum operations like entanglement and state generation with improved efficiency.

## Contribution

The authors develop a QSP-based approach to create non-Gaussian gates with higher accuracy and fixed interaction time, extending capabilities beyond existing SNAP gates.

## Key findings

- Generated a new non-Gaussian gate with phase shift depending on boson number.
- Achieved higher accuracy within fixed, short interaction times.
- Extended QSP formalism to non-unitary operations like noiseless amplification.

## Abstract

Non-Gaussian operations are essential for most bosonic quantum technologies. Yet, realizable non-Gaussian gates are rather limited in type and generally suffer from accuracy-duration trade-offs. In this work, we propose to use quantum signal processing (QSP) techniques to engineer non-Gaussian gates on hybrid qumode-qubit 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 the boson number. This gate reproduces the selective number-dependent arbitrary phase (SNAP) gates under certain parameter choices, but with higher accuracy within a short, fixed and excitation-independent interaction time. The gate unlocks new applications, for example, in entangling logical qudits and deterministically generating multi-component cat states. Additionally, our versatile QSP formalism can be extended to systems with other interactions, and also engineer non-unitary operations, such as noiseless linear amplification and generalized-parity measurement.