# Deterministic nonlinear gates with oscillators mediated by a qubit

## TL;DR

This paper proposes a method to implement nearly deterministic and high-fidelity nonlinear operations on harmonic oscillators using a two-level system, overcoming limitations of measurement-based approaches.

## Contribution

It introduces a sequential interaction scheme with a two-level system to realize nonlinear gates, such as self-Kerr and cross-Kerr, with high success probability.

## Key findings

- Achieves near-deterministic nonlinear operations
- Demonstrates implementation of self-Kerr and cross-Kerr couplings
- Uses feasible dispersive coupling in realistic setups

## Abstract

Quantum nonlinear operations for harmonic oscillator systems play a key role in the development of analog quantum simulators and computers. Since a variety of strong highly nonlinear operations are unavailable in the existing physical systems, it is a common practice to approximate them by using conditional measurement-induced methods. The conditional approach has several drawbacks, the most severe of which is the exponentially decreasing success rate of the strong and complex nonlinear operations. We show that by using a suitable two level system sequentially interacting with the oscillator, it is possible to resolve these issues and implement a nonlinear operation both nearly deterministically and nearly perfectly. We explicitly demonstrate the approach by constructing self-Kerr and cross-Kerr couplings in a realistic situation, which require a feasible dispersive coupling between the two-level system and the oscillator.