7 papers
Mirror codes: High-threshold quantum LDPC codes beyond the CSS regime
Andrey Boris Khesin, Jonathan Z. Lu
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcti…
SpiderCat: Optimal Fault-Tolerant Cat State Preparation
Andrey Boris Khesin, Sarah Meng Li, Boldizsár Poór +3
The ability to fault-tolerantly prepare CAT states, also known as multi-qubit GHZ states, is an important primitive for quantum error correction. It is required for Shor-style synd…
Universal graph representation of stabilizer codes
Andrey Boris Khesin, Jonathan Z. Lu, Peter W. Shor
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis…
Average-Case Complexity of Quantum Stabilizer Decoding
Andrey Boris Khesin, Jonathan Z. Lu, Alexander Poremba +2
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all…
SET! From Groups to Games
Andrey Boris Khesin, Tanya Khovanova
The game of SET is one of the best mathematical games ever. It is no wonder that people have tried to generalize it. We discuss existing generalizations of the game of SET to diffe…
Graphical quantum Clifford-encoder compilers from the ZX calculus
Andrey Boris Khesin, Jonathan Z. Lu, Peter W. Shor
We present a quantum compilation algorithm that maps Clifford encoders, encoding maps for stabilizer quantum codes, to a unique graphical representation in the ZX calculus. Specifi…