Searching for relations between different physical processes is one of the most successful ways of doing science. Usually these relations are not only surprising but also useful as they offer us a different approach to certain problems. In statistical mechanics such a relation was showed by Christopher Jarzynski [1] who found an equality connecting equilibrium information with non-equilibrium measurements for finite classical systems.

From thermodynamics we know that in the case of quasi-static or, in other words, processes which take an infinitely long time the work done on the system is equal to the difference of Helmholtz free energy of the system. However, for finite time processes some proportion of the work can be dissipated and so in general the total work may surpass the difference of Helmholtz free energy.  Jarzynski’s result shows it still possible to find the value of that difference from finite time measurements which actually makes the whole thing accessible experimentally [2].

To give you some taste how it is done, Jarzynski simply uses the special method of averaging the exponential function of work. This approach provides better weights for different work trajectories to get at the end the mean value of the exponent of dissipated work equaled to one.  It occurs that from Jarzynski’s equality it is easy to derive the fluctuation-dissipation relation as well as the already mentioned inequality between average work and the difference of the system’s free energy.

One interesting question recently asked by researchers was whether there are quantum analogues of this result.  Reported positive answers only prove the general importance of Jarzynski’s equality.

[1] C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997).

[2] J. Liphard et al., Science 296, 1832 (2002).

In Douglas Adam’s Hitchhikers guide to the Galaxy, the author describes a race of hyper-intelligent beings who built a super-computer whose purpose is to compute the Answer to the Ultimate Question of Life, the Universe, and Everything. The computer, christened Deep Thought by its architects, famously gave the answer to be 42. The creators now have a huge problem: they have the answer, but what does the answer really mean?

Now, I am not writing this because I have secret aspirations of being a philosopher. In fact, I tend to run away in uncontrolled panic as soon as a philosopher steps into my peripheral vision. No, the real reason why I thought of Hitchhiker’s Guide is because some scientists right now have a similar problem right now. Except we are not hyper-intelligent beings.  And the computer is not really that super.

On May 2011, a company called D-Wave Systems announced a device called the D-Wave One, declaring it the world’s first commercially available quantum computer. Quantum computing has long been touted as one of the next big revolution in computing technology.  The basic promise of a quantum computer is easy to understand: Problems that may take years or decades using a classical computer may potentially be solved in hours or days using a quantum computer. A closer look will tell you that this does not necessarily apply to every problem you would like to solve, but hey, nobody ever reads the fine print anyway.

In any case, D-Wave may claim that they are selling a quantum computer, but can we really know for sure it is really quantum? If you are purchasing a multimillion dollar device, it kind of makes sense to do some checks to make sure you are not blowing all that cash on snake oil. As it stands, the ‘quantum computer’ in question does give out an answer if you give it the right kinds of questions, but what does that answer really mean? That is what scientists like Sergio Boixo et al.  (arXiv:1304.4595) are trying to find out. So far the results appear to support D-Wave’s claims in that it does indeed appear to be quantum, but skepticism remains. Still, ignoring the controversy a little bit, it is perhaps interesting to discuss a little bit about the science behind how the D-Wave One is supposed to work.

The basic idea behind D-Wave’s system is Quantum Annealing. Annealing takes its name from a process with the same name in metallurgy. When you cast steel, a sudden temperature change can lead to internal irregularities that stresses and weaken the material. By heating the steel at an intermediate temperature and cooling it, it allows to metal to rearrange itself in the atomic level so that it becomes more homogeneous, and stronger.

The same idea goes behind Quantum Annealing. The idea is to have lots of tiny little magnets called spins that possibly interacts with each other. Ordinarily, this configuration of spins may occupy a high energy state instead of the lowest energy state called the ground state. Classically, spins can get stuck in this higher energy state because they don’t have enough energy to get out of it. This is where the annealing portion comes in. To make sure that the spins occupy the ground state, one can heat up the system, giving the spins enough energy to reconfigure themselves such that they can enter a lower energy state, and then slowly decreasing the energy of the system. The quantum part of the process comes from the fact that the spins can occupy a superposition of states or be entangled with one another, in addition to being able to tunnel between energy states which are classically not allowed. The process ends when the spins occupy the lowest energy configuration, the ground state.

Now, this appears to have nothing to do with computation. Where is the answer to the computations? What is the problem being computed? Well, both the question and the answer turn out to be the ground state of the system.  It just so happens that when the number of spins get large, it becomes computationally very difficult to find out the ground state, but relatively simple to perform the Quantum Annealing process and just measure the ground state coming  out of it. So D-Wave’s system can only solve computational problems that can be modeled by a system of interacting spins, and where the desired answer is the ground state configuration of such a system of spins. This sounds a bit restrictive, and indeed it is, but that’s the device D-Wave is selling, and the only such device on the market, if it is not a complete fake of course.

One thing’s for sure though:  it isn’t going to give us the the Answer to the Ultimate Question of Life, the Universe, and Everything anytime soon.

Individuals usually lead fairly solitary lives; except on the occasions when they congregate for social activities, like, baseball or football. On these occasions they demonstrate a type of collective behavior which is motivated by their interests.
Do you know that we can find the same phenomenon in quantum physics? Distinguishable noninteracting particles work separately. However after interacting with another distinguishable particle, they often work together and demonstrate collective behavior. We call these phenomena composite particles. Do you know any of the well-known composite particles in physics? Ubiquitous examples include anyons, and cobosons. But there are a plethora of other examples which inspire a rapidly developing field of research.