Last Thursday, at the QIP rump session in Beijing, John Smolin described recent work with Graeme Smith and Alex Vargo [SSV] showing that arbitrarily large numbers $latex N$ can be factored by using this constant-sized quantum circuit
to implement a compiled version of Shor’s algorithm. The key to SSV’s breathtaking improvement is to choose a base for exponentiation, $latex a$, such that the function $latex a^x bmod N$ is periodic with period 2. (This kind of simplification—using a base with a short period such as 2, 3, or 4—has in fact been used in all experimental demonstrations of Shor’s algorithm that we know of). SSV go on to show that an $latex a$ with period 2 exists for every product of distinct primes $latex N=pq$, and therefore that the circuit above can be used to factor any such number, however large. The problem, of course, is that in order to find a 2-periodic base $latex a$, one needs to know the factorization of $latex N$. After pointing this out, and pedantically complaining that any process requiring the answer to be known in advance ought not to be called compilation, the authors forge boldly on and note that their circuit can be simplified even further to a classical fair coin toss, giving a successful factorization whenever it is iterated sufficiently many times to obtain both a Head and a Tail among the outcomes (like having enough kids to have both a girl and a boy). Using a penny and two different US quarters, they successfully factor 15, RSA-768, and a 20,000-bit number of their own invention by this method, and announce plans for implementing the full circuit above on state-of-the art superconducting hardware. When I asked the authors of SSV what led them into this line of research, they said they noticed that the number of qubits used to do Shor demonstrations has been decreasing over time, even as the number being factored increased from 15 to 21, and they wanted to understand why. Alas news travels faster than understanding—there have already been inquiries as to whether SSV might provide a practical way of factoring without the difficulty and expense of building a large-scale quantum computer.
Pop goes the discord bubble
Well, the rat is out of the bag; Schroedinger’s Rat, that is. That’s the new quantum blog by Miguel Navascues and boy is it snarky! I was keeping it under my hat for a while so I could enjoy it privately, but the time has come to announce it to the world. Miguel is fearless about shouting his colorful opinions from the rooftops, and I can respect that, even if I don’t agree with everything he says.
Miguel’s second post is all about quantum discord. As anyone who reads quant-ph knows, there are around two or three papers per week about discord for years now. Unfortunately, a huge number of these are nearly worthless! Quoth the Rat:
The quantum discord of a bipartite state was first defined by Ollivier and Zurek as the difference between its original quantum mutual information and the same quantity after we perform a rank-1 projective measurement on one part.
Now, what does that mean? Probably, nothing. But lack of motivation has never prevented investigation at international scale. And so we ended up with one more research topic that clearly goes nowhere, in the line of entanglement sudden death…
If you thought he was exaggerating, here is a paper that has been cited 263 times since May 2009: Robustness of quantum discord to sudden death. Wow, discord is immortal! And in case you want more, you can just go to quantumdiscord.org and find a list of discord papers and see for yourself.
Before we can treat the patient we have to understand the disease, and this is exemplified by a typically test case: Quantum discord for two-qubit X-states (cited 256 times). The authors compute the quantum discord and a few other entanglement measures for a family of two-qubit states and conclude that there is no obvious relationship between the various measures. Why did they do this? “Because it’s there” might have been a good reason to scale Everest, but this feels more like a homework assignment for a graduate course. Wait, I take that back: Scott’s students’ homework is much more interesting and relevant.
But Steve! What about all the good discord papers? You can’t just trash the entire field!
You’re absolutely right, there are good discord papers. I can even name about 5 of them, and I’m willing to bet there are as many as 12 or 15 total. My intention is definitely not to trash the subject as intrinsically uninteresting; rather, I want to highlight the epidemic of pointless papers that constitute the discord bubble. I hope that thinning the herd will increase the quality of the results in the field and decrease the hype surrounding it, because it has really gotten completely out of control.
Here are some good rules of thumb for those moments when you find yourself writing a discord paper. If you are calculating something and you don’t know why you are calculating it, then close your latex editor. You do not have one of the good discord papers. If the discord you calculated is not related to a resource (physical, computational, etc.) in a quantifiable way, you probably don’t have a good discord paper. If it is related to a resource, but you had to concoct that relationship in a totally ad hoc way that doesn’t generalize, then you do not have a good discord paper. Ditto if the relationship is via a protocol that literally nobody cares about. If you only have two qubits, you almost certainly don’t have a good discord paper. Good theory papers usually have $latex n$ qubits. And if your weak theory result suffers from one or more of the above but you add in some equally unimpressive experimental results to cover up that fact, then you absolutely, unequivocally do not have a good discord paper. I don’t care what journal it’s published in, it is not a good paper and you should be ashamed of yourself for inflating the bubble even further.
As bad as the authors are, this bubble is also the fault of the referees. Simply being correct is not enough to warrant publication. It also has to be new, non-trivial, and interesting. Please referees, “Just Say No” to papers that don’t meet this standard!
Enough of this bad medicine. In the comments, feel free to mention some of the actually good discord papers, and why they deserve to keep their value after the bubble bursts.