When I switched into quantum computing for my Ph.D. topic, one of the the first research questions that my (former) supervisor, Dr. Richard Cleve, had asked me was whether the adversary method for quantum lower bounds applied in the Hamiltonian oracle model.
The answer is “yes”.
It took me a while to figure this out, and in retrospect the answer is (maybe) obvious.
I think this question is a very nice example of a research question for a beginning Ph.D. student, in that it’s not too difficult, and at the same time could potentially lead to a body of research culminating in a Ph.D. (Although this didn’t happen for me.)
I had been meaning to put my research notes online for a while, but had put it off because they’re not as useful to as many people as they could be, in the form that they’re in.
(I had actually wanted to put all of my research notes online from the very beginning, but refrained from doing so because I didn’t want my parents to find out that I was studying quantum computing, since they had threatened to disown me if I did so. But now that they have disowned me, I no longer have a reason not to write about quantum computing in public.)
In this next series of posts (which might be interspersed between posts about other things), I’m going to write about the experiences I went through, and the topics that I learned, while trying to answer the above question. I’m also going to clean up the relevant sections of my research notes, and post them online, along the way. I hope that my posts and research notes will be useful not only to other quantum computing researchers, but also to potential graduate students in any theoretical field who might have to undergo similar experiences when they begin their research.
I’ve created a page on my wiki where my notes on this research question will eventually go.
Interestingly, I’ll be inadvertently implementing the Quantum Pontiff’s idea of a delayed open notebook, since the research I’ll be writing about took place about three years ago.
– davinci 11744
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