Scalable Qumode-Qubit State Transfer and Fast-forward Quantum Fourier Transform using Oscillators

Transferring the information stored in the expansion coefficients of a multi-qubit state to the coefficients of a continuous-variable state is an important protocol for communicating quantum information. It was shown in previous work how to transfer an n-qubit state to a single qumode in mathcal{O}\(2ⁿ\) time. We show that by transferring this state to m qumodes, the runtime can be improved to mathcal{O}\(2^n/m\). Furthermore, we demonstrate how multi-qumode state transfer can be used as a subroutine for approximately realizing the n-qubits quantum Fourier transform on m-qumode with runtime scaling mathcal{O}\(m2^n/m/ε+m²\), accelerating qubit quantum Fourier transform using qumodes. This work presents a scalable approach to convert discrete and continuous quantum information between an arbitrary number of qubits and qumodes. It represents a crucial step forward in mixed analog-digital quantum signal processing for computing, sensing, and communication.