Binary codes enable better fault tolerant gates for quantum computers
Asymptotically good binary triorthogonal codes and higher-level transversal gates
Information Theory
Summary
Quantum computers need special error-correcting codes to run certain operations safely. This paper shows how to build sets of such codes that work well as they get larger, specifically for a kind of operation called transversal gates at high levels of complexity. The authors used advanced math to create these codes and turned them into practical binary codes for use in quantum computing. Their work also helps improve the process of generating very clean quantum states, which is important for making quantum computing more efficient.
What this means in practice
- •For quantum computing engineers: Design fault-tolerant quantum processors that implement complex gate layers more reliably using these new binary error-correcting codes supporting transversal gates.
- •For quantum hardware developers: Reduce resource costs for producing high-quality quantum gate states via improved distillation protocols derived from these codes.
Authors
Rodrigo San-José
Abstract
For each level of the Clifford hierarchy from the third level onward, we construct explicit asymptotically good binary CSS codes supporting diagonal transversal gates in that level. We achieve this using algebraic geometry codes over binary extension fields and performing an alphabet reduction that translates orthogonality conditions over the extension field to binary overlap conditions. In particular, we obtain the first asymptotically good family of binary triorthogonal codes. We also give a stronger construction with worse parameters for which no subsequent correction is required. Finally, adapting an error-correction-based distillation protocol, our binary $T$-gate families yield constant-overhead $T$-state block distillation under sufficiently weak input noise and ideal stabilizer operations.