Tuesday, April 21st, 2026
1:00pm – 1:50pm
Stratton Hall 301
Speaker: Bill Martin, WPI
Title: Quantum stabilizer codes
Abstract: Microsoft reports that current implementations of quantum computing devices exhibit error rates about 1-in-100 to 1-in-1000 gate operations. By contrast, standard CPUs measure errors per billion or per trillion operations. Even the simplest broadly deployed algorithms entail millions of operations, making error rates below 1-in-a-million unworkable. This is why, informally speaking, each logical qubit must be encased in a protective shell of physical error-correcting qubits. This talk, while surveying a few recent developments, will focus on an overview pf quantum stabilizer codes. We will work from first principles, using only linear algebra over the complex numbers and over finite rings. The Weyl-Heisenberg group for an n-qubit quantum system is the group of 2^n by 2^n matrices formed by taking tensor products of 2 x 2 Pauli matrices in all possible ways. If G is an abelian subgroup of the Weyl-Heisenberg group, then the matrices in G are simultaneously diagonalizable. Each maximal common eigenspace of the matrices in G is a quantum stabilizer code. The talk will outline how these codes can be constructed, how they can be used, and their error-correction abilities.