# Synthesizing multi-phonon quantum superposition states using flux-mediated three-body interactions with superconducting qubits

## TL;DR

This paper proposes a scheme to control a quantum mechanical resonator using superconducting qubits, enabling the preparation of non-classical states and entanglement, advancing quantum technology integration.

## Contribution

It introduces a tunable three-body interaction scheme for quantum control of mechanical resonators with superconducting qubits, including ground-state cooling and state preparation.

## Key findings

- Demonstrates ground-state cooling of the mechanical resonator
- Achieves high-fidelity non-classical state preparation
- Enables qubit-phonon entanglement with negative Wigner functions

## Abstract

Massive mechanical resonators operating at the quantum scale can enable a large variety of applications in quantum technologies, as well as fundamental tests of quantum theory. Of crucial importance in that direction, is both their integrability into state-of-the-art quantum platforms as well as the ability to prepare them in generic quantum states using well-controlled high-fidelity operations. Here, we propose a scheme for controlling a radio-frequency mechanical resonator at the quantum scale using two superconducting transmon qubits that can be integrated on the same chip. Specifically, we consider two qubits coupled via a capacitor in parallel to a superconducting quantum interference device (SQUID), which has a suspended mechanical beam embedded in one of its arms. Following a theoretical analysis of the quantum system, we find that this configuration, in combination with an in-plane magnetic field, can give rise to a tuneable three-body interaction in the single-photon strong-coupling regime, while enabling suppression of the stray qubit-qubit coupling. Using state-of-the-art parameters and qubit operations at single-excitation levels, we numerically demonstrate the possibility of ground-state cooling as well as high-fidelity preparation of mechanical quantum states and qubit-phonon entanglement, i.e. states having negative Wigner functions and obeying non-classical correlations. Our work significantly extends the quantum control toolbox of radio-frequency mechanical resonators and may serve as a promising architecture for integrating such mechanical elements with transmon-based quantum processors.