Co-authored by BTQ Chief Quantum Officer Dr. Gavin K. Brennen, the research introduces a new error-correction framework for permutation-invariant codes—an enabling step toward more reliable quantum ...

Abstract: Permutation codes are vector quantizers whose codewords are related by permutations and, in one variant, sign changes. Asymptotically, as the vector dimension grows, optimal Variant I ...

Abstract: In this paper we prove new lower bounds for the maximal size of permutation codes by connecting the theory of permutation codes with the theory of linear block codes. More specifically, ...

# This small notebook implements, in [Python 3](https://docs.python.org/3/), several algorithms aiming at a simple task: # given a certain list, generate *all* the ...

The order of permutation of 0,1,2,3 is [0,1,2,3], [0,1,3,2], [0,2,1,3], [0,2,3,1], [0,3,1,2], [0,3,2,1], [1,0,2,3], [1,0,3,2], [1,2,0,3], ...

python.sort() # Sorts in ascending order..reverse() # Reverses the list in-place. = sorted() # Returns a new sorted list. = reversed() # Returns reversed iterator. python.insert(, ) # Inserts item at ...