Over a year in the making, the mega paper about continuous variable cluster states has finally been published on the archives. Titled, `Quantum Computing with Continous Variable Clusters‘, the paper is essentially a refinement of the idea I jointly proposed as a first year PhD student that it would be pretty cool to have an formulation of measurement based computation where each node was a quantum harmonic oscillator.

Though the idea seemed fairly second nature at the time (hey, just take qubits and replace them with optical modes!), the level of interest in it has been quite a pleasant surprise. The second follow-up paper aims at polishing the idea, and includes a lot of the details that was sort of brushed away during the initial proposal.

Quantum Computing with Continuous-Variable Clusters
Mile Gu, Christian Weedbrook, Nicolas C. Menicucci, Timothy C. Ralph, Peter van Loock

Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.

Arxiv Link

Not the most exciting paper, but it has pretty pictures, including my first ever attenmpt at doing rendering wtih 3D studio max. That’s got to be worth something right? Also, I must thank Christian Weedbrook, who capacity in eliminating all of my typos as I busily hammered away at furniture here in Singapore is so remarkable that I’m convinced he secretly hides a quantum computer in his back yard!

So… there I was, the guinea pig of the new `research siminar’ series, where members of the Center for Quantum Technology presented their work in progress to public, in an effort to improve inter-department collaboration. Such political correctness, and so good on paper! Yet, you still want to give a talk with no major loopholes, and that not an easy task for you’re giving a 1 hour presentation on 4 days of work! Yet, somehow, I persevered (though my sleeping patterns did not), and all animations prepared. The notebook plugged in… the presentation ready to execute….

Yet, the $15,000 dollar presentation system laughed, and proceeded to perform the blue screen of death. So, yup, the entire session ended up being a whiteboard presentation. So, here’s the promised digital version, totally free and available online! The basic idea is thus:

Occam’s Razor states that the few assumptions an explanation makes, the more preferable and likely it true. When applied to modelling the output of a string of bits from a black box, one interpretation measures the simplicity of a given by the number of bits that the model must keep track of to execute. The fewer the number of bits, the sharper the razor. Crutchfield then showed that the sharpest of classical razors was the Epsilon machine… our question is, can Quantum mechanics sharpen that razor further? 

• Classical and Quantum Razors (321)

The talk first reviews how classical Occam’s Razor can be formalised through use of Epsilon Machines, and proceeds to outline some of my thoughts on how a Quantum version of Occam’s Razor could be superior. I hope to have a nice article on this stuff in a next few days. In the mean time, feel free to make sense of the presentation! There’s obviously lots of holes to fill, and in fact, Valerio pointed out one during the talk… see if you can find it too, but I promise that its already been addressed!

One of my current research projects have lead me to an rather interesting side problem. The basic idea is this:

If you’re given some random data streams from an unknown physical object… can you make a good argument to say that the object works on quantum principles? Obviously, there’s always a classical explanation, given that classical computers can simulate quantum computers, albeit inefficiently. However, could you call upon Occam’s Razor and argue that the simplest explanation is quantum?

To do this, one needs first a good mathematical formulation of Occam’s Razor for classical systems. It turns out that one good candidate are what’s called epsilon machines. So, I thought I’d write a quick research note of these objects:

• Epsilon Machines: Formalizing Occam’s Razor

Now… just need to find a meaningful way of quantizing it!