Multi-Qumode-Qubit State Transfer and the Quantum Fourier Transform

Transferring a quantum state between continuous-variable (CV) qumodes and discrete-variable (DV) qubits is a useful subroutine for for quantum communication between qubit chips or for accelerating qubit-based algorithms by running selected subroutines that are more efficiently carried out using native qumode gates. Previous work has detailed how one may transfer a multi-qubit state to a single qumode and how this can be used to implement the quantum fourier transform on qubits by native free-evolution of the qumode. However, the runtime of that protocol scales exponentially with the number of qubits n as O(2ⁿ). We show that by transferring the state to an m-qumode system, this exponential scaling can be reduced to O(m2^n/m+ m²) while maintaining the deterministic nature of the protocol, thus achieving a time and space tradeoff in this important subroutine for hybrid CV-DV quantum computing. Notably, when the ratio of the number of qubits to the number of qumodes is kept constant, this exponential scaling factor becomes a constant multiplicative factor. We further demonstrate how this multi-qumode state transfer procedure can be used to implement the quantum fourier transform. This demonstration provides a path towards accelerating qubit-based algorithms more broadly by taking advantage of the high-dimensional nature of qumodes.