Impure Quantum Codes: Applications and Bounds

CS/Math Seminar - Andrew Nemec, Duke University.

Impure quantum error-correcting codes display interesting properties not found among classical codes, such as having multiple low-weight errors map to the same syndrome. In this talk, we will look at how these codes can be used to design good variants of quantum codes, such as quantum-classical hybrid codes and quantum data-syndrome codes. Additionally, we prove a new Hamming-like bound for impure stabilizer codes, that is stronger than the normal quantum Hamming bound. This new bound must hold for all t-error-correcting codes of length greater than some integer N(t), and we use it to show that only a handful of code lengths allow for impure distance-3 stabilizer codes encoding an optimal number of qubits.

QNC 1201 + ZOOM

https://uwaterloo.zoom.us/j/98197825051?pwd=T0JxY051cUM3MGpXdWJnb1NCZHpnQT09

Meeting ID: 981 9782 5051
Passcode: 908775