P. Oscar Boykin

My co-authors Meera Sitharam, Mohamad Tarifi, and Pawel Wocjan and I put a new preprint on the Arxiv today: Real Mutually Unbiased Bases. This work considers MUBs over the reals. In this case, we can get interesting upper and lower bounds on the number of real MUBs in each dimension. The problem seems to be rather different than the complex case, due to the discrete nature of real MUBs.

Hopefully, this approach could give us new insight into finding bounds for complex MUBs.

This is a quick note that I did go and make it back from DSN 2005. It was a nice trip to Yokohama, Japan. Please feel free to look at my slides on Reversible Fault Tolerant Logic. You can find the paper in the Arxiv:: Reversible Fault-Tolerant Logic.

I would be very interested in a new kind of GNU/Linux distribution. For many people, maintaining a system is not something they would care to do. They do not want to be burdened with system administration or don’t have the skills to do the job properly. What I propose is something like the Linux Terminal Server Project for home users. I am not suggesting that the software run on a remote server and display locally, but that the systems boot from a remote NFS server. The software is run locally, but installed and maintained on a remote server.

Here is how the system works:

• User obtains a boot-cd to start up his system (this is like an install disk).
• Like a live-CD, the system automatically configures the hardware. But unlike a live-CD, the system makes use of the local disks.
  The first time the user starts the system, she is asked if she wants to use part of her disk to speed up performance (highly recommended), and if she would like to use part of the disk to keep her personal files. If the user says no, we are back into the normal live-CD mode, and forget everything, but if the user wants to use the disk, things can get interesting.
• The disk is used for two things: caching a remote read-only NFS file system, and storing the users home directory. The CD contains the most recent snapshot of the remote NFS file system (or the most commonly used parth thereof).
• The cache is initialized with the CD data.
• From then on, the system runs all software from the server. An NFS caching mechanism makes sure not to transfer files if they are up to date in the local cache.

The user never installs any software, never does any updates, and never does any system administration. If there is some update that requires a reboot, a msg can be presented to the user to notify her to restart as soon as possible, but otherwise, such updates will take effect at the next boot.

This system is a dedicated desktop environment. As such, one can get rid of root completely.
Since hardware is configured automatically, and a huge selection of software is already installed, the user has no need or ability to do anything that requires root access (assuming we allow any local user to restart the computer).

This is apt-get without user intervention to get packages, or Click-N-Run except, just Run.

Clearly this is not for everyone, but for many home and corporate users, this system would be an easy to use, easy to maintain, cheap to deploy system. If it has all the Debian Packages, I would probably run it.

I recently put a new preprint on the Arxiv: Reversible Fault-Tolerant Logic. This is a joint work with Vwani Roychowdhury which considers fault tolerance techniques for reversible computing. We show that as long as the reversible gates have errors less than a threshold value, those errors may be held in check by using O(N \log^{4.75} N) noisy gates to simulate N noise-less gates.

This work also considers the case of locally connected architectures in 1-D and 2-D. There we show that the threshold decreases somewhat. Finally, we consider the entropy that must be removed from the system and see that the entropy saving aspect of reversible computing is lost unless the gate error rate is much lower than the threshold error rate.

I will present this work this summer at the International Conference on Dependable Systems and Networks.

New preprint on the Arxiv: “Threshold Error Penalty for Fault Tolerant Computation with Nearest Neighbour Communication”. Catchy title huh? This is actually a nice paper in my opinion. It shows how to do fault tolerant quantum computing with a 1-d array of qubits. We find various error thresholds depending on different assumptions, the range is from 10^(-4) to 10^(-7) (probability of gate error per time step). These can be improved somewhat.

A nice compliment to this work would be a project to carefully study the physics of some proposed quantum computing models and see what the attainable error rates are likely to be. Is 10^(-7) totally out of the question? Can we find some cases where bit error rates will be higher than that even in principle? It would be interesting to do some analysis akin to Asher Peres, Petra F. Scudo and Daniel R. Terno’s “Quantum entropy and special relativity” to find cases were the error rates will be above threshold even in principle.

I am preparing for my trip to DSN 2004, the International Conference on Dependable Systems and Networks. I will be presenting our paper: Fault Tolerant Computation on Ensemble Quantum Computers. This is joint work with Tal Mor, Farrokh Vatan, Vwani P. Roychowdhury. I leave this Friday and return on the fourth of July.