Fast Bosonic Control via Multiphoton Qubit-Oscillator Interactions

Bosonic quantum computation exploits the infinite-dimensional Hilbert space of a harmonic oscillator to protect quantum information. This protection typically arises from symmetries in the codespace, such as invariance under specific rotations or displacements. In this work, we present a protocol for preparing oscillator states with n-fold rotational symmetry, some of which are logical codewords for bosonic quantum error correction. The protocol relies on a multiphoton interaction between the oscillator and an auxiliary qubit. Further, we achieve arbitrary control over the oscillator's Hilbert space by using a combination of different multiphoton interaction orders, constituting a significant extension to the Law and Eberly state synthesis protocol. Results show that the use of multiphoton qubit-oscillator interactions can substantially reduce the state preparation time, in comparison to the linear qubit-oscillator interactions that are usually employed. We also discuss the preparation of multi-oscillator states using a generalized variant of the protocol. To validate the robustness of our protocol, we perform numerical simulations in the presence of qubit and oscillator relaxation and dephasing using realistic planar superconducting circuit parameters. Our findings have the potential to significantly improve the performance of bosonic codes on planar superconducting hardware, which are an almost inevitable necessity for scalable bosonic fault-tolerant superconducting quantum computers.