Quantum computing and quantum optics with recoiled free electrons

TL;DR

This paper introduces a novel quantum platform using recoiled free electrons interacting with optical fields, enabling quantum simulation, information processing, and hybrid electron-photon state engineering.

Contribution

Derives an exact recoil-resolved interaction Hamiltonian for free electrons, enabling universal quantum computation and advanced quantum simulation applications.

Findings

Recoil ladder forms a high-dimensional qudit with programmable couplings.

Single electron can realize multiple logical qubits and high-fidelity gates.

Engineered ladder transitions create nonclassical light correlations.

Abstract

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.