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Cavity quantum electrodynamics (QED), wherein a quantum emitter is coupled toelectromagnetic cavity modes, is a powerful platform for implementing quantumsensors, memories, and networks. However, due to the fundamental tradeoffbetween gate fidelity and execution time, as well as limited scalability, theuse of cavity-QED for quantum computation was overtaken by other architectures.Here, we introduce a new element into cavity-QED - a free charged particle,acting as a flying qubit. Using free electrons as a specific example, wedemonstrate that our approach enables ultrafast, deterministic and universaldiscrete-variable quantum computation in a cavity-QED-based architecture, withpotentially improved scalability. Our proposal hinges on a novel excitationblockade mechanism in a resonant interaction between a free-electron and acavity polariton. This nonlinear interaction is faster by several orders ofmagnitude with respect to current photon-based cavity-QED gates, enjoys widetunability and can demonstrate fidelities close to unity. Furthermore, ourscheme is ubiquitous to any cavity nonlinearity, either due to light-mattercoupling as in the Jaynes-Cummings model or due to photon-photon interactionsas in a Kerr-type many-body system. In addition to promising advancements incavity-QED quantum computation, our approach paves the way towards ultrafastand deterministic generation of highly-entangled photonic graph states and isapplicable to other quantum technologies involving cavity-QED.

Universal and ultrafast quantum computation based on free-electron-polariton blockade