12 problems

Fix $t$, and let $n$ be large enough that the parameters $m_2,\ldots,m_t$ defined by … where $c\in(-1,1)$ is chosen so that $\sum_i m_i=n+1$. Let $H$ be the Tanner-code parity-chec…

Let $(j_Z,j_X,k)$ be any balanced triple satisfying … The corresponding HA-side and MN-side classical constituent codes are the codes associated with this triple, and a balanced tr…

QTS isomorphism conjecture. The isomorphic nature of the two disjoint subsets results in a set of qubits at level $2$ of $T(v_r)$ for every $v_r\in V_i$, which limits the qubit sep…

Bravyi's conjecture. Higher products of CSS codes with good distance should exist.

A $d_v$-$3$, $d_c$-$6$ QLDPC code is a quantum low-density parity-check code with variable-node degree $3$ and check-node degree $6$. An interconnected 6-cycle structure is a struc…

The $B3$ code is a quantum LDPC code whose one circulant matrix is composed of juxtaposed $6$-cycles and whose other circulant matrix has girth $10$. Girth-10 performance conjectur…

A $d_v$-$3$, $d_c$-$6$ GHP code is a code with variable-node degree $3$ and check-node degree $6$. A $(6,0)$ trapping set is a trapping set containing $6$ variable nodes and no uns…

A $d_v$-$3$, $d_c$-$6$ GHP code is a code with variable-node degree $3$ and check-node degree $6$. A weight-$3$ polynomial is a polynomial having three nonzero terms, and a juxtapo…

Let $s$ be the current error $0$-chain in the bundle complex, and let its bundle projection be a $0$-chain in the base complex. A $1$-chain $w$ in the base complex is required to s…

Let $d_Z$ denote the $Z$-distance of the quantum LDPC code, and consider the proposed homology-decoding algorithm described in the paper, which uses local updates by fiber strings…

Let the quantum LDPC codes be constructed from the classical LDPC codes employed in the paper. A quantum error-correcting code is degenerate if a nontrivial Pauli operator of weigh…

Entanglement-assisted stabilizer codes use maximally entangled states, or ebits, to import classical binary or quaternary linear codes into the quantum setting. The entanglement-as…