Quantum computing and quantum optics with recoiled free electrons

Free electrons interacting coherently with optical fields provide a powerful platform for quantum simulation and quantum control. For kiloelectron-volt electron energies, even optical photon emission and absorption produce appreciable quantum recoils, endowing the electron with a discrete and controllable energy ladder. Starting from relativistic quantum electrodynamics, we derive an exact recoil-resolved interaction Hamiltonian in a traveling wave picture. The resulting recoil ladder forms a high-dimensional qudit with programmable couplings and sufficient controllability for universal quantum computation. We demonstrate applications to quantum simulation, including one-dimensional analogue black-hole models including Hawking radiation physics, and to quantum information processing, where multiple logical qubits and high-fidelity gates can be realized with a single electron. In parallel, the same recoil-enabled dynamics enable the controlled creation of complex hybrid electron–photon states, in which engineered ladder transitions imprint nonclassical correlations and structure onto the emitted light. Together, these results establish recoiled free electrons as a versatile platform bridging quantum optics, Hamiltonian engineering, and quantum simulation.