Divisible Codes for Quantum Computation

Understand

Divisible codes are defined by the property that codeword weights share a common divisor greater than one.

• They are used to design signals for communications and sensing, and this paper explores how they can be used to protect quantum information as it is transformed by logical gates.
• Given a CSS code $\mathcal{C}$, we derive conditions that are both necessary and sufficient for a transversal diagonal physical operator $U_Z$ to preserve $\mathcal{C}$ and induce $U_L$.
• The group of $Z$-stabilizers in a CSS code $\mathcal{C}$ is determined by the dual of a classical $[n, k_1]$ binary code $\mathcal{C}_1$, and the group of $X$-stabilizers is determined by a classical $[n, k_2]$ binary code $\mathcal{C}_2$ that is contained in $\mathcal{C}_1$.