Shaping and Controlling Quantum Photonic States Using Free Electrons

Continuous variable quantum computing is a rapidly developing field both theoretically and experimentally. It provides a promising approach for fault-tolerant quantum computing while enabling error correction using bosonic codes, such as GKP codes. 

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, and are always limited in coherence time by matter ancilla qubits.

We show how the fundamental coherent interaction of free electrons and photons, perhaps the most basic interaction in QED, provides the necessary building blocks for quantum information processing. Recent advances in ultrafast electron microscopy enable the coherent shaping of free-electron wavefunctions into qubits and qudits, measurement of light statistics, coherent control of two-level systems, and generation of entanglement. Electron qubits fundamentally differ from other matter ancilla qubits: they are flying qubits, 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 (>30%) with no need for feed-forward. Moreover, we show that further electron interactions enable readout, error correction, and universal control over the GKP state. By interacting with multiple GKP states, the free-electron can create multi-qubit gates, with which we propose schemes for creating multipartite highly entangled states, such as GHZ states and cluster states.