High-dimensional Antimony Atoms in Silicon for Photonic Entangled State 'Machine Gun' Quantum Error Correction

Silicon-based quantum hardware is compatible with the standard semiconductor manufacturing industry and has high gate fidelities for 1- and 2-qubit operations, above 99%. However, scaling up to many physical qubits remains a challenge, especially in academic research facilities. In 2009, Lindner and Rudolph introduced an alternative quantum computing paradigm called the Photonic Cluster State Machine Gun. This approach links the spin of a single electron with photons emitted from a quantum dot. By coupling n emitted photons with the electron’s spin, an n + 1-qubit linear cluster state in one dimension is created, allowing for the generation of large-scale linear cluster states comprising many qubits. Our work advances this approach by using the antimony (123Sb) donor in a silicon-based semiconductor spin qudit platform which encompasses a 16-dimensional Hilbert space comprising the spin 1/2 electron and the spin 7/2 nucleus. In the context of the machine gun, we view antimony as the quantum dot itself. Due to its multi-level energy structure, a single antimony atom can emit up to 7 different frequency photons through electric dipole transitions, enabling the creation of multi-qubit entangled photonic states. We analyze these states with respect to foliated quantum codes. The machine gun technique allows for a greater number of effective qubits in donor spin qubits in silicon, enabling Quantum Error Correction and facilitating the transition from reliable small-scale hardware to larger quantum computers