Binary codes with special gates improve quantum error correction methods
Asymptotically good binary triorthogonal codes and higher-level transversal gates
Information Theory
Summary
Correcting errors in quantum computers is very important but challenging. This paper presents new ways to build special binary codes that help perform certain quantum operations more easily and reliably. The authors use advanced math techniques to create these codes, which are better than previous versions. Their work also improves methods for preparing key quantum resources, potentially making some quantum processes more efficient.
quantum error correctionbinary codesClifford hierarchytransversal gatesCSS codesalgebraic geometry codestriorthogonal codesT-gatestate distillationstabilizer operations
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.