Abstract
It is known that nonadditive quantum codes can have higher code dimensions than stabilizer codes for the same length and minimum distance. The class of codeword stabilized codes (CWS) provides tools to obtain new nonadditive quantum codes by reducing the problem to finding nonlinear classical codes. In this work, we establish some results on the kind of non-Pauli operators that can be used as observables in the decoding scheme of CWS codes and propose a procedure to obtain those observables.
Highlights
It is known that quantum computers are able to solve hard problems in polynomial time and to increase the speed of many algorithms [1, 2, 3, 4]
The framework of stabilizer codes was used to obtain a large class of important quantum codes [9, 10, 11]
We describe a procedure to find these observables, which is specially useful for CWS codes that are close to stabilizer codes
Summary
It is known that quantum computers are able to solve hard problems in polynomial time and to increase the speed of many algorithms [1, 2, 3, 4]. The framework of stabilizer codes was used to obtain a large class of important quantum codes [9, 10, 11]. A code is called a stabilizer code if it is in the joint positive eigenspace of a commutative subgroup of Pauli group. In certain cases, these codes are suboptimal, because there is larger class, called nonadditive codes. We describe a procedure to find these observables, which is specially useful for CWS codes that are close to stabilizer codes.
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