Using Third Quantization and High-spin Donors for Photonic Entanglement without Entangling Operations

There are two main families of hardware for building large-scale, fault-tolerant quantum computers: matter-based and photonic hardware. Entanglement in matter-based systems, such as semiconducting platforms, is achieved through interactions between qubits. Consequently, fault tolerance in these systems has focused on stabilizer states, which are relatively easy to realize by applying two- or multi-qubit gates.

However, photons interact extremely weakly, leading to the challenge of probabilistic entanglement, where entangling photons through direct interactions is highly inefficient. Remarkably, creating entanglement deterministically with photons is quite feasible. As Rudolph proposed, it is possible to spread single photons into multiple modes, creating mode entanglement. Through the use of only local unitaries and classical communication, we can achieve sufficiently useful entanglement for universal computation. This approach is known as the "Third Quantization" formalism. This formalism receives independent single photons as input and outputs (high-dimensional) entangled states without using any entangling operations(stabilizer states)

We propose an experiment using high-dimensional antimony donor in a silicon chip to demonstrate the smallest feasible implementation of third quantization and explore its features. Starting with a single matter-based atom, we generate high-dimensional entangled photonic states that align with Rudolph’s third quantization formalism.