I will be in the San Francisco Bay area from July 12 to July 19. I'll be staying in the Mountain View area, and looking for housing around there, for August (ideally) or September (less ideally) move-in. If you want to hang out with me while I'm around, or if you have housing tips, or know someone who needs a housemate, reply here. :-)

Qubits and P-bits

I have heard the refrain "everyone would understand quantum mechanics, if only it were explained thusly!" a surprising number of times recently, and I want to explore one such value of "thusly": The idea that quantum mechanics is just what falls out if you allow probabilities to be negative. (See e.g.)

I like the idea behind the Scott Aaronson link above -- and I think he's a crazy-smart guy with some great ideas -- but I think his explanation is still more technical than it has to be. He starts with the idea that the rules of quantum mechanics are just what probability would be, if you allowed negative probabilities; but then he immediately heads from probability into quantum, and starts talking about 2-norms and stochastic matrices.

I want to focus on going the other way: what if we took all the stuff we do in quantum, the same way we do it in quantum, but did it with ordinary probabilities instead? Thus, the p-bit -- "probabilistic bit" -- instead of the qubit.

Much like a qubit, which is 0 or 1 with some amplitudes, a p-bit is 0 or 1 with some probabilities. You can think of it as the result of flipping a biased coin, which comes up heads with some probability p, and tails with some other probability q. (You're jumping out of your seats trying to tell me that q = 1-p. Yes, I know, but there's a nice pattern which will fall out from not doing that just yet, so sit down.)

So adopting the same notation we use for qubits, in which |0> represents the zero-bit and |1> represents the one-bit, we can say that |0> is a p-bit, as is |1>, and so is 0.5|0> + 0.5|1>. Unlike qubits, of course, all the coefficients must be positive and real. Like qubits, p-bits have a normalization constraint: the coefficients, representing probabilities, must sum to 1.

When we put all this out in the open, the first interesting thing we see is that p-bits, just like qubits, display entanglement! Of course, in classical probability, we just call it correlation. Consider, for example, the system in which my friend flips a (fair) coin; then sets another coin next to it, so that both have the same side up; and doesn't tell me anything. If |0> is heads and |1> is tails, the coins are together in the state 0.5|00> + 0.5|11>: they are perfectly correlated, or "entangled" if you will. This kind of entanglement looks a lot less creepy than the quantum version, though. If you reveal one of the coins, you do immediately know the value of the other one; but it's clear that this is because they were the same all along. In physics terms, they share a "hidden variable". It appears, meanwhile, to be the case that quantum entangled states are more powerful than can be explained by a theory with purely local interactions, and hidden variables; informally, we can show that the states were not merely "the same all along".

P-bits also have the same property that qubits do, of having information "in the implementation" that can't be externally observed. If we look at a system that involves flipping coins to produce bits, this is the same as saying that, given just the results of the coinflips, we don't immediately know the probability distribution from which they were drawn. An interesting thing to note here is that the "no-cloning" rule in quantum physics appears to be outside of, and separate from, the math. Our p-bits here are purely mathematical, but we could imagine a physical implementation of them which also obeyed the "no-cloning" rule. In such a system, given an unknown "state" (i.e. an unknown probability distribution over bits), we'd be allowed to "observe" it once (i.e. take a sample from the distribution, and see what bits we get), but the result would not be enough to tell us what the original "state" (distribution) was.

Of course, p-bits do not demonstrate one other creepy phenomenon that qubits do, which is superposition. A p-bit has no phase: It can only be in |0>, or |1>, or some mixture of the two. This means no interference effects either. (Superposition is not as creepy when you consider that any superposition, is actually a pure state if you look at it in the right basis. But in any case, the only basis available for p-bits is the |0> |1> basis.)

I guess the conclusion I draw from all of the above is this: some of the difficulty traditionally associated with quantum mechanics comes from the complexity of the math, and some comes from unrelated parts of the physics. I don't know whether this approach has been taken before, but it seems to me that it could make a lot of sense, when teaching quantum, to start by teaching about what the world would look like if it were made of p-bits, and then introduce qubits as a revision of that world. What say you to this?


I guess I ought to make a PSA here: I am officially funemployed! By which I mean, I have departed from Google (of my own free will), and do not currently have anything else to replace it with. (Don't tell my grandmother. She'll kill me.) I'm planning to take a few months off, and then move out to the SF bay area around the time my lease expires in August.

While I'm funemployed, I'm going to post daily updates to LJ on what I'm getting up to with my life, so you can all help keep me on track and doing useful things. ;-) If you are interested in reading said updates, please comment so I can put you on the filter. But be warned; they may at times be deadly boring, or incomprehensible, or both. (The first two, for yesterday and today, will be about Bitcoins, hardware, and Cirque du Soleil.)


I am going to Frostburn!

It is a Burning-Man-related camping event, taking place over a weekend in February.

Are any of you going? If so, want to camp together? :-)


Unrelated postscript: I have a bunch of topics in mind I've been meaning to write about. This seems like a good place to publish such things. So watch this space soon for essays on topics about which I have no authority to say anything, but have something to say anyway. ;-)

Random acts of baking

My house now contains chocolate chip cookies. I made them using this recipe:

I also have some cookie dough still, having only baked the first batch of them, since I only have one baking sheet at the moment.

If you are willing to come all the way out to Friendship just for some delicious homemade cookies, let me know and you are welcome to some. :-)

My trip to NYC for HOPE

TL;DR: Airlines suck, but I made it to HOPE despite them. Running ethernet cable is fun.

So I've been in New York for HOPE this weekend. It's been pretty fun! But the trip to get here was a bit chaotic...

I was supposed to fly from PIT to LGA at 7:30. But in the early afternoon, I got a text informing me my flight was delayed to 8:30. Eyeroll. Then I got another one telling me 9:15. I left for the airport at 7ish, and as soon as I got on the bus got another one saying 9:45.

At this point I figured the flight was probably going to be cancelled, so I pulled out my laptop on the bus over and looked up alternative flights. The only real candidate was one through PHL leaving at 8:45 (and arriving at midnight, more than an hour after even the thrice-delayed flight I was supposed to be on.)

So as I sat there contemplating asking them to move me onto the other fight, since I expected my flight was going to get cancelled -- I got the text saying my flight was cancelled. This was just as I got to the airport, so I went up to the ticket counter and asked them to put me on the other flight. Well, it was full. I asked for standby, but the guy told me he couldn't put me on standby on a flight with a connection, because if I didn't get on the connection it would strand me in PHL. Why I would prefer to be stranded at my point of origin, rather than my much closer point of connection, is a mystery to me, but he was very steadfast about it.

So, I had him book me on the 5:45 AM flight the next morning, figuring I'd have dinner and sleep at the gate. He warned me that I might not be able to get through security with my boarding pass for the next day; he was intending to suggest I eat and sleep outside security, but I instead pulled out my boarding pass for the cancelled flight, figuring security ought accept it, and had no problem.

So before eating dinner, I went straight to the gate of the PHL flight for a last-ditch attempt to go out the same night. Before approaching the gate agent, I checked something online that I'd had a sudden suspicion about; sure enough, the flight from PHL to LGA was NOT FULL. The asshole at the front desk could have booked me on it, to let me fly standby to PHL. I do wonder if maybe he was prohibited from suggesting it to me if I didn't ask for it; he kept emphasizing that he couldn't put me standby on PIT-PHL because I was "not confirmed on the PHL-LGA flight". Maybe he was hinting I should ask to be; I dunno.

Anyway, I made the same request of the gate agent, emphasizing that there were open seats on the second leg and asking her to book me on it, and sure enough she let me fly standby, and I made it onto the plane. \o/ Unfortunately I spent all my dinner time negotiating to get on a plane instead. :-( And double-unfortunately, when I had to check my bag because they were out of overhead space, I forgot to take my wallet out of it. No dinner for me in PHL either.

So here comes the happy part of my tale. When I asked the flight attendant if there was any way to get my hands on my checked-to-LGA bag in PHL, she asked why and I told her about the wallet (and my desire to eat in PHL). She absolutely insisted on giving me $8 out of her own pocket (all she had on her) and a huge 1L bottle of water from the drink cart. Thus I was in the end able to feed myself in PHL, thanks to a random stranger's kindness! \o/ (As an amusing aside, I came up with a scheme by which I could feed myself in PHL without my wallet; order food for delivery to the terminal at PHL, using my card on file at Campusfood, and go out through security to pick it up. I wouldn't have had time to pull it off, though.)

So from that point on things went pretty smoothly. My luggage with my wallet in it showed up on time in LGA; I caught a bus to train to the Hotel Pennsylvania, with some minor hitches (the train was actually partially replaced by a bus, due to construction; and I got lost and went to the wrong subway platform, costing me $2.25; and then I waited past two trains that would have taken me to my destination because I thought they were the wrong ones.) But basically everything was smooth and I got there in one piece! So yay!

I don't plan to write about HOPE itself, because there's really not nearly as much exciting to say as about the trip to get there. ;-) But I will mention that I finally got to the Hotel Pennsylania at 2AM, and was immediately drafted to crimp and run ethernet cable until about 5AM. It was a pretty good time. ^_^

Selling furniture, books, other stuff

Photos of some items here:

Everything must go by Tuesday.

I am selling:
- desks (all depicted above)
- dressers (all depicted plus one more in the basement)
- bookshelves (all depicted above)
- random furniture-bits (nightstand, other stuff)
- chairs (4 wobbly wooden dining room chairs, one nice wooden desk chair, one kind of shitty desk chair)
- futon -- slightly broken, but fixable (mattress and frame, depicted separately)
- another futon-pad-thing, no frame
- mattress and box springs, twin; box springs are pretty saggy
- microwave
- toaster oven
- toaster
- small 4 cup coffee maker
- george foreman grill
- whatever other assorted crap I find myself needing to get rid of
- lots of as-yet-unsorted books

Name-your-own-price. Let me know what you're interested in. The condition of most of it is "eminently useable, but not good as new."

I also have a bunch of books to get rid of, but I don't have them cataloged yet. If you want to come by my place, you can look through them; otherwise I will be cataloging them today and tomorrow and listing them, hopefully.