1. Progress in Quantum Convolutional and Subsystem Codes Andreas Klappenecker This research was supported by NSF CAREER award 0347310 and NSF grant 0622201

2. Motivation The main obstacles to successful quantum information processing are unwanted interactions between quantum bits and their environment. This poster discusses results concerning subsystem codes (interesting for fault tolerant quantum computing) quantum convolutional codes (interesting for quantum communication)

3. Appetizer: Sphere-packing Bound A classical error-correcting code is a subspace of {0,1} n. If it can correct t errors, then spheres of radius t about the codewords must be disjoint. Dividing the (total #words is the space) by (the #words in a sphere of radius t) yields an upper bound for the #codewords in a t-error correcting code.

4. Quantum Stabilizer Codes A pure [[n,k,d]] stabilizer code satisfies the sphere-packing bound. Do there exist impure stabilizer codes beating the sphere-packing bound? Often conjectured, but all evidence speaks against this conjecture.

5. Subsystem Codes A quantum error-correcting code is a subspace C of the state space. A subsystem code imposes further structure by decomposing the subspace into a tensor product C = A ­ B, encoding information only into subsystem A. We settle the open problem whether subsystem codes can beat the sphere-packing bound. Come see the poster to find out about this and other open problems that we have solved.