Comparing Schemes for Creating Qudit Graph States from 16- & 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 non-deterministic measurement technique - these linear graphs can then be combined to form more complex resource states (multi-photon 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 CZ 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.

💡 Research Summary

This paper presents a comparative study of two hardware approaches for generating arbitrary high‑dimensional qudit graph states using antimony (¹²³Sb) donors in silicon. The antimony donor possesses a nuclear spin I = 7/2, giving an eight‑dimensional nuclear Hilbert space, and when bound to an electron (S = 1/2) the combined system spans a 16‑dimensional space; two such donors together provide a 128‑dimensional space. The authors investigate (i) a single‑donor scheme that creates linear qudit cluster states deterministically via sequential photon emission, and then stitches these linear pieces together into more complex resource states (rings, ladders, etc.) using non‑deterministic, destructive fusion measurements; and (ii) a two‑donor scheme in which the donors share a common electron and are directly coupled by high‑dimensional controlled‑Z (CZ) gates, thereby eliminating the need for intra‑graph fusion.

The paper begins by reviewing the requirements of fusion‑based quantum computing (FBQC): a supply of entangled photonic resource states and a set of fusion operations that probabilistically join these states. While FBQC has been explored extensively for qubits, photons naturally support qudits because they can occupy multiple modes. High‑dimensional graph states are defined by weighted edges corresponding to powers of the CZ gate, and they enable more efficient error‑correcting codes (e.g.,