Public defence, Communications Engineering and Networking Technology, MSc Dawei Jiao

Title of the thesis: Pairs of CSS Error Correction Codes with Transversal Gate Implementation

Thesis defender: Dawei Jiao
Opponent: Prof. Narayanan Rengaswamy, University of Arizona, United States
Custos: Prof. Olav Tirkkonen, Aalto University School of Electrical Engineering  

Unlocking universal quantum computing through cross-code interaction

Realizing universal fault-tolerant quantum computation is one of the greatest challenges in physics, largely due to a fundamental limitation: the Eastin-Knill theorem. This theorem dictates that no single quantum error correction code can perform all required logical operations in a direct, fault-tolerant (transversal) manner. While existing workarounds, such as magic state distillation, provide a viable path forward, they demand massive overhead in both physical qubit counts and processing time. This thesis explores a different strategy: instead of relying on a single code, it introduces a "cross-code transversality" framework that allows entirely distinct quantum codes to interact directly and efficiently.

Moving beyond conventional single-code systems, the thesis derives the mathematical conditions required for multi-qubit gates (such as CNOT and CZ) to operate fault-tolerantly between different codes. This theoretical breakthrough enables transversal code-switching and leads to the design of a novel hybrid system supporting a transversal Toffoli gate—a capability mathematically proven to be impossible within any single-code architecture. The practical utility of this framework is demonstrated across three key applications: optimizing quantum repeaters for long-distance communication via a mirrored code structure, minimizing resource overhead during code switching, and distilling high-fidelity Toffoli states without relying on resource-intensive "T-magic" states.

Numerical simulations under realistic noise models confirm that these cross-code methods drastically reduce the physical hardware and circuit depth required for fault-tolerant operations compared to traditional protocols. The results offer a new perspective on quantum computing: rather than searching for one perfect code, integrating diverse code families into a single system is the key to scalability. This approach provides a practical, resource-efficient roadmap for realizing universal quantum computers.

Thesis available for public display 7 days prior to the defence at Aalto University's public display page.

Key words: Quantum Computing, Quantum Error Correction