Hardware-Aware Quantum Error Correction and Architectural Designs for Quantum Computers

Quantum Error Correction (QEC) is often idealized as hardware-agnostic, yet its practical implementations must be tailored to the underlying system. The nuclear and electron spins of donor atoms in silicon constitute a physical platform that offers long coherence times, a well-characterized Hamiltonian, precise quantum control, and a readout mechanism that uses the electron as an ancilla. In this thesis, we reconsider the fundamentals of QEC, from gates to architecture, showing how they can be tailored to donor spins, while exploring different architectural paradigms using donor spins. Motivated by the hardware’s native Hamiltonian and ancilla-assisted readout, we design Single-Step Parity Check (SSPC) gates that perform parity checks directly, bypassing 1- and 2-qubit decompositions and improving circuit error tolerance. We developed a numerical workflow using experimental process matrices to evaluate these operations and quantified cumulative losses in a two-body parity-check circuit by tracking 1- and 2-qubit gate error rates on a two-phosphorus, one-electron silicon chip. GRAPE-optimized pulses were generated for both standard and SSPC-based circuits on the same platform, showing SSPC gates outperform and offer hardware-aware QEC implementations. We next explore antimony, a high-spin donor, as a candidate for photonic quantum computing. With a nuclear spin of 7/2, antimony has eight energy levels which, when coupled to a microwave cavity, can emit a single-photon across eight modes. This supports third quantization, where (near-)deterministic photon entanglement is achieved by spreading single photons across many modes and sending each mode to a party, creating entanglement without photon–photon interactions or probabilistic gates. We proposed an experiment for the simplest realization of third quantization, where an antimony donor produces two independent 8-mode photons, distributed to parties, creates a Bell state between 56 random pairs with 87.5% efficiency. We then explored high-dimensional fusion operations for fusing qudit cluster states. Focusing on Type-II fusion, a central component of measurement-based quantum computing, we derived the most efficient high-dimensional protocol known to date — a 723-fold improvement over the best previously known protocol in the case of d = 5. To further enhance success probability of fusion, we introduced extra-dimensional corrections framework. We unified these insights to design two approaches for qudit graph state generation using antimony donors. One is for the direct generation of arbitrary graph states from coupled antimony donors, where two antimony atoms share a single electron, forming 128-dimensional Hilbert space, while the other focuses on the generation of linear graph states from a single antimony donor, followed by high-dimensional fusion operations to construct graph states in arbitrary shapes. We compared the two schemes in terms of their capabilities and potential for scalability.