Back of the Envelope

I'm thinking of getting some business cards. Not for work, but for blogging. Of course, by "get," I mean design them with Microsoft Publisher and buy some business card stock and print them out on my color inkjet at home. That's really all that's needed to get business cards these days. In any case, here are a couple of designs I came up with.

First design:


Second design:

What do you think? You notice that they're both based on the new Back of the Envelope logo I now have on my page (if it looks like the old one to you, hit reload to make sure the new image is used rather than the old one you have in your cache). I decided to update it to a better looking envelope with a more quantum computation-specific equation. <0|+>=1/2^½ is actually a dot product of two vectors (one-dimensional arrays). If |0> and |1> are the two qubit states zero and one in vector form, then <0| and <1| are their conjugate transposes. (That's just what it sounds like--take the conjugate of the complex numbers and transpose the vector.) Using the usual 0 and 1 basis, we define the vector |0>=[1;0] and |1>=[0;1]. (The semicolons indicate that the elements are in separate rows--it's hard to show here.) Thus, <0|=[1 0] and <1|=[0 1]. <0|0>=1 and <1|1>=1, but <0|1>=0 and <1|0>=0. It's an orthonormal basis set, where each vector has a unit length and is orthogonal to the other vectors in that set, and by multiplying them by scalars you can create any vector in that space. Meanwhile, |+>=1/2^½(|0>+|1>) and |->=1/2^½(|0>-|1>), forming a separate orthonormal basis set. I've discussed different bases before. The key idea is that while |0> and |1> are orthonormal to one another, as are |+> and |->, |0> and |1> are not orthonormal to |+> amd |->, giving <0|+>=1/2^½.