Topic
Quantum LDPC codes
6 records: 6 unsolved, 0 solved. Filter the catalog by this topic →
-
Asymptotically good quantum locally testable codes
Does there exist an infinite family of qubit CSS codes with linear rate and linear distance whose check matrices have uniformly bounded row and column weights and constant soundness?
Unsolved -
Good quantum LDPC codes with a non-Clifford transversal CCZ gate
Do there exist triples of qubit CSS LDPC codes with linear combined rate and linear distance on which the transversal CCZ gate induces a non-Clifford logical operation?
Unsolved -
Linear-size logarithmic-depth encoders for good quantum LDPC codes
Does some family of asymptotically good qubit CSS LDPC codes admit unitary encoding circuits with linearly many gates and logarithmic depth?
Unsolved -
Distance of constant-rate quantum XYZ product codes
Do there exist quantum XYZ product codes, built from classical parity-check matrices with uniformly bounded row and column weights, that have constant rate and minimum distance of order \(N^{2/3}\) on \(N\) physical qubits?
Unsolved -
Square-root distance bound for weight-four stabilizer codes
Is there a universal constant \(C>0\) such that every qubit stabilizer code that encodes at least one logical qubit, and whose stabilizer group is generated by Pauli operators of weight at most four, has distance at most \(C\sqrt n\) on \(n\) physical qubits?
Unsolved -
Quantum LDPC codes at the Pauli hashing bound
For which probability vectors \(\mathbf p=(p_I,p_X,p_Y,p_Z)\) can quantum low-density parity-check (LDPC) stabilizer codes reliably attain the exact hashing rate over the Pauli channel?
Unsolved