Multi-qubit entanglement and quantum processing within ququart

Quantum technology, leveraging non-classical characteristics, enables breakthroughs in computation, communication, and metrology. Entanglement generation is fundamental. However, efficiently creating large-scale entanglement remains challenging. Using 2 n physical modes within a single particle has been exploited for encoding n -qubit entanglement, yet this approach is believed to be unscalable. Here, using sequentially quantum correlations on a single particle, we present a Ququart Encoding scheme to encode and process multi-qubit entanglement within ququart. We implement a programmable integrated-photonic entanglement generator on a silicon chip, encoding up to 5-qubit entanglement and quantum circuits within 2 ququarts. Within a ququart, we generate high-fidelity 3-qubit W and Greenberger-Horne-Zeilinger states and verify quantum teleportation and phase estimation. Encoding a pair of entangled photons as ququarts yields a 5-qubit Greenberger-Horne-Zeilinger state at 688 Hz, with fidelity 0.956 ± 0.053, confirming genuine 5-qubit entanglement. While the 2 n physical-mode overhead persists for general purposes, our scheme reduces it from exponential to linear under certain circumstances, potentially accelerating large-scale quantum systems.