Free Electrons as a Universal Tool for Photonic Quantum Computation

An approach for fault-tolerant quantum computers is encoding quantum information in continuous variables, which enables error correction using bosonic codes, such as GKP states. The generation and manipulation of these states require physical nonlinearities, which are hard to come by in optical frequencies. So far, GKP states have been demonstrated only in microwave frequencies, with matter ancilla qubits limiting the coherence times.

Recent advances in ultrafast electron microscopy enable the coherent shaping of free-electron wavefunctions into qubits and qudits that fundamentally differ from previously proposed matter ancilla qubits: free-electrons are flying qubits; they interact with multiple spatially separated photonic modes and implement ultrafast coupling that does not limit coherence times.

Here we propose using the strong interactions of free-electrons with light as a source for optical cat and GKP states. Our approach enables the generation of optical GKP states with above 10 dB squeezing at a high post-selection probability. Moreover, we show that the interaction enables readout, error correction, and control over the GKP state. Additionally, by interacting with multiple GKP states, the free-electron qubit can be used to create multi-qubit gates. We propose a scheme for creating multipartite highly entangled states, such as GHZ states and cluster states, for quantum communication and measurement-based quantum computation.