The Quantum Pontiff

Well it’s been two weeks and I have had absolutely zero time to think about scirate. (It was midterm week!) So far 71 users have registered. Whoop! I have certainly slowed down the progress of science (what do you think this blog and scirate.com is for, after all?) So what were the highest scited papers in the time preiod Jan 23-Feb 6?
7 votes: quant-ph/0701173 [abs] Quantum walks on quotient graphs by Hari Krovi and Todd A. Brun
7 votes: quant-ph/0702031 [abs] A scheme for demonstration of fractional statistics of anyons in an exactly solvable model by Y.J. Han, R. Raussendorf, and L. M. Duan.
6 votes: quant-ph/0701165 [abs] A precise CNOT gate in the presence of large fabrication induced variations of the exchange interaction strength by M. J. Testolin, C. D. Hill, C. J. Wellard and L. C. L. Hollenberg
6 votes: quant-ph/0702020 [abs] How much of one-way computation is just thermodynamics? by Janet Anders, Damian Markham, Vlatko Vedral and Michal Hajdusek
5 votes: quant-ph/0701149 [abs], quant-ph/0702008 [abs]
The first papers with 7 votes, quant-ph/0701173, explores the role symmetries of a graph play in (discrete) quantum random walks on theses graphs. Of course whenever a physicist sees the word “symmetries” the immediate reaction should be “change basis”! Indeed for a proper choice of coin in the quantum random walk, the symmetries of the graph (the group of automorphisms) can be inherited by the unitary operator discribing the evolution of the quantum random walk. Whenever you have a unitary operator which is symmetric under a representation of a group, then, via Schur’s lemma, you know that this unitary operator will have a very nice form. Indeed if you decompose the representation into its irreducible irreps, then the unitary operator can only have support over the space of degeneracies of a given irreducible irrep. So, for the quantum random walks, this means that the walk will be confined to a particular subspace. In the setup considered in the paper this works out to be a walk on the quotient graph obtained from the original graph and some subgroup of the automorphism group. Very fun stuff. The authors then go on to analyze hitting times, worry mostly about the case of inifinite hitting times. They develop a criteria for spotting when the walk on the quotient time is not infinite (building on some prior work.) Okay, so what’s the next step? At what point can you identify when the walk will have fast hitting times would be nice. Also can you use the above arguments to spot when classical walks will be exponentially slower?
The second paper with 7 votes, quant-ph/0702031 is four pages, so it must be going to PRL 😉 The basic idea of this paper is fairly straightforward. The authors point out that it is easy to think about generating the ground state of Kitaev’s toric code using methods within experimental reach in ion traps and in optical lattices. This prepared state can then be used to “demonstrate” anyon statistics. In other words, instead of preparing a state in Kitaev’s toric code by cooling to the (degenerate) ground state, one can just prepare such a ground state using a simple quantum circuit, perform the braiding operations, and observe the effects of the (abelian) anyon statistics. Okay, so let me play the devil’s advocate here (something I don’t do well since I’m a coward.) Should we really claim that this is would constitute a “demonstration of fractional statistics of anyons”? My worry here is with the word “anyon” which, it seems, we usually restrict to things which are quasiparticle excitations. Of course this may just be a matter of taste, but I’d be curious to hear what others think. On a less subjective, and more concrete point, one interesting issue which was not addressed in the paper (at least on my admittedly fast first reading) was how errors will propogate in the scheme described for preparing the Kitaev state. Is it true that the preparation is in any way fault-tolerant? For example if you’re doing this in ions is it really possible with current two gate fidelities to demonstrate this in the 6 qubit setting? Interestnig stuff! How long before one of the experimental groups gets to exclaim “fractional statistics” after performing a few thousand experiments 🙂 ?
Okay, enough Scirate pimping. Let’s see what the next round of papers bring (how long before ideas hatched at QIP hit the presses? 🙂 )