Comparing schemes for creating qudit graph states from 16- and 128-dimensional Hilbert space using donors in silicon

In this work, we compare two schemes for generating arbitrary qudit graph states using spin qudits in silicon. The first scheme proposes the creation of qudit linear graph states from a single emitter—a silicon spin qudit. By employing fusion—a destructive and nondeterministic measurement technique—these linear graphs can then be combined to form more complex resource states (multiphoton entangled states), such as ring or ladder structures, which are used to carry out the computation. The second scheme employs two spin qudits. Instead of relying on fusion, the two emitters are directly coupled via controlled-Z gate to generate the same resource states, thereby eliminating the need for fusion. We compare the two schemes in terms of their ability to produce equivalent resource states and discuss their respective advantages and limitations for building scalable architectures.