Orthogonal Geometry and Quantum Error Correction
by
A.R. Calderbank
AT&T Labs, Florham Park, NJ

Quantum effects are seldom evident in today's electronic devices since the quantum states of many millions of atoms are averaged together blurring their discreteness. But in quantum computing the foundations of quantum mechanics are finding direct and visible application in information processing. The unreasonable effectiveness of quantum computing is founded on coherent quantum superposition or entanglement which allows a large number of calculations to be performed simultaneously. This coherence is lost as a quantum system interacts with its environment and an important challenge today is to devise means of preserving it.

A quantum error correcting code is a way of encoding quantum states into qubits so that error or decoherence in a small number of individual qubits has little or no effect on the encoded data. This talk will describe a beautiful group theoretic framework that simplifies the presentation of known quantum error correcting codes and greatly facilitates the construction of new examples.

Date received: February 3, 1999