Quantum Science and the Next Step in Computation

It's a common situation: You are at a party, going out with friends or just met someone on the bus stop and start chatting. Small talk. What are you doing here? Nice / horrible weather today, isn't it? So, what do you do? Well, there it is. I find myself hesitating to answer this question. I guess many have, at least those, that write in science blogs. I work in experimental quantum physics and there is only so many witty comebacks to stunned silence, bewilderment or statements that they never got physics. But that's okay, it's clearly not for everyone. But luckily I have a great comeback when people ask me what it's for.

Look around you and you will see the fruits of quantum physics all around you. From the semiconductors that make up basically everything around us that runs on electricity to computers and smartphones. None of it possible without quantum science. While it still is spooky and weird, it has silently worked its way into our everyday lives. And it still does, working tirelessly in the background to maybe, some day, save the day again. Not the hero we know, but the hero we need?

Approaching the end of the line

Because there is trouble brewing and that has to do with smartphones, too. What was the New York Times for the commuter of the 40s is now the portable device, the tablet and the phone. Even watches and fridges want to log on to the internet to share your heart rate with the world or check for replacement milk. Big data is a thing growing powerful. And while the world grows smaller with all of us having each other within a touchpad's reach and the knowledge of mankind just a paywall away, there are those of us who wonder how long this will keep on going.

Mankind is starting to fall behind in the race between the growing demand of communication bandwidth and computational power and what it can supply. Since the last revolution in communication and computation which arguably was the integrated circuit and then digital communication, we have gotten by with improving these technologies. Build smaller units, build more units, multiplex and expand. But Moore's law can only take us so far and once we have single atom transistors, which people have been working on for more than a decade already, there is no (non-particle collider based) way to make a smaller one.

And anyone who has been frustrated at seeing their computer struggle to perform a task with one core at full load while the others are contemplating taking an afternoon nap knows that adding units does not necessarily speed things up. Even when they work together, the more units you have, the more work goes into coordinating them working together. The management must have its cut, so to say.

For scientists this problem is already there. Many computations (foremost in quantum mechanics) grow in complexity exponentially fast with number of elements. That is really bad. In fact, how bad it is is almost not fathomable for mankind, which caused Albert Allen Bartlett's famous quote:

"The greatest shortcoming of the human race is our inability to understand the exponential function."

To put this into some context, consider the simulation of a system with 128 elements takes 0.1 minutes. 200 elements will take still less than a minute, 256 will take 5 minutes, 300 will take 20 minutes. How long will it take for 512? How long for 1024? The correct answers would be in the order of 10 and 200,000 years. 2048 elements would take about 1.21e19 years. The estimated age of the universe is 1.38e10 years. Hacking RSA encryption coincidentally scales very similar to that, so with a 512 bit key you are pretty much set, barring someone handing out the private key.

With fundamental limitations starting to rain into our parade, we have to come up with alternative solutions and nowadays the words 'Quantum computation' and 'Quantum Simulation' are seen more and more often in this context.

While the term 'quantum' is often mistreated (not only by quantum healing. I struggle to see where the quantum part comes in with cosmetics or dishwasher tablets), in this particular instance it is worth having a closer look. Even with the sheer amounts of money being poured into quantum information science and everything related to quantum computation; even with the publicity attracted by Google and the (in)famous D-Wave, there is very little knowledge out there of what people are actually talking about when they say 'Quantum Computation' and 'Quantum Simulation'.

Simulators and Computers

First of we should make clear what the words mean, so let's forget about the quantum bit for a minute and get back to that aspect later. When we say simulation, we mean to say that we make a system imitate what another system does. We can study the simulator to find out what another, real-life thing would do. The idea is not new at all, although in abstracts like this, it may be hard to see why this is useful at all.

A nice example why simulators are useful is minimal surfaces: Minimal surfaces is a branch of mathematics that got stuck with this name for historical reasons, but let's stick with the obvious thing and talk about actual surfaces that are in a physical sense minimal. For example, the minimal surface area or the minimal energy of a surface that is formed between wires. Mathematicians and physicist study these for many reasons, but one for example that doesn't involve two extra paragraphs of explanation is making very stable roofs.

While the study itself often involves variational calculus and differential geometry, in two and three dimensions there is excellent simulators that are actually used to test the predictions made. Take some metal wire, fold your frame (for example the support structure of the roof you want to build) and put it in soap solution. Take it out and the soap will form thin films or bubbles that form minimal surfaces.

While predicting and studying may be hard, the soap film does not care how difficult we find it. It just is minimal due to the laws it obeys. And because tent roofs obey the same (or very similar) laws, we can use the tiny soap-and-wire model to simulate how we should build stadiums.

Another example is an analogue finance simulator. Before the advent of digital computing, predicting the evolution of financial products or even an economy as a whole was almost impossible. However, fluid dynamics can be used to predict how money flows around and in 1949 the Kiwi William Phillips build the MONIAC; a device that featured water tanks, pipes and pumps of different sizes and pumping powers to simulate the economy of the United Kingdom. While it seemed odd at first, it turned out to be an excellent model and economists actually studied what would happen if taxation was increased/decreased (increase or decrease some pump rates) or interest rates were altered. Again, the simulator was modeling a different system that was harder to study and it had no difficulty in doing that because it just evolved due to the physical laws it had to obey.

Now to draw the very important distinction between the simulator and the computer. Can we make MONIAC run Super Mario? No, we cannot. But we can make a computer run it. And we can make the computer emulate MONIAC such that it gives the same behaviour. In fact, MONIAC is in a museum now because digital computers are more convenient to have in your office than a huge tank and pump assembly. Simulators are very good at a specific task, but cannot work outside their parameter regime; whatever may limit it. Computers can in principal do any calculation, although they may be very much slower than a specialized simulator.

Putting in some quantum

So what's so new and great about the quantum in quantum simulation and quantum computation? An example that is often provided to demonstrate the difference in classical (i.e. non quantum) and quantum computation is prime number factorization using Shor's algorithm and its application to hacking RSA encryption. As pointed out earlier, the time it takes to crack RSA encryption grows exponentially with the number of bits for the encryption (technically it's super-polynomial) on a classical computer. Using Shor's algorithm on a hypothetical quantum computer would reduce the time to polynomial. While this doesn't sound too impressive, it means reducing the time for 1024 bits from being measured in units of the age of the universe to hours or days.

This had many implications if realized and not the least of them being the utter collapse of contemporary data security. Of course, where there is quantum computation, quantum cryptography isn't far away. But it turns out, building a quantum computer is not easy. Of course, we need different building blocks for a quantum computer (or simulator) than for a classical one. One that is talked about most often is the quantum bit (qubit). A classical bit (which could be implemented as the charge state of a MOSFET) can have one of two states: 1 or 0, charged or discharged. A quantum bit uses the quantum property of superposition, which means that the bit can be 1, 0 or any mix between 1 and 0. What we mean when we say 'mix' is a bit tricky. Suffice it to say for the moment that, if I had 1000 qubits that are identically in a state that is 30% in 1 and 70% in 0 and I would measure all 1000 of them, there is a very high chance I found that 300 would be in 1 and 700 in 0.

A better picture would be to say that a classical bit can take one of two points on a line. In a Cartesian coordinate system, imagine this line to be the z axis. A qubit now can be anywhere on a sphere, which is the famous Bloch sphere interpretation. We went from being able to take 2 points on a line (let's be generous and call this 1D) to infinitely many points on a sphere (which is 3D). The alert reader may point out that analogue data is also continuous and can take on any value between 0 and 1. Turns out we (=mankind) went for digital because it is technically less challenging to do all the fancy multiplexing and other techniques and work with 1 and 0 then trying to distinct between 0.3663719 and 0.3663720 . But it would be negligent not to mention that the same problem arises on the Bloch sphere, where it may be just as hard to discern between closely spaced states.

So how do we put the quantum in the simulator or computer? What are those qubits made of? There are many different angles people use to approach the problem and as of yet there isn't one single implementation that is clearly the best. There is superconducting circuits, trapped ions, entangled photons, nitrogen vacancy centers and more unconventional potential qubit candidates. All of them have some advantages and some disadvantages. All are not perfect (yet). So what stops us from making quantum computers?

Apart from the plethora of challenges around making good qubits, there is plenty of other challenges left that need to be mastered before we can have a working quantum computer. (Whether Google and the D-Wave have one or not is very much contested and I will not discuss this.)

Quantum Simulation

But as with the analogue simulator that spearheaded the simulation of financial evolution, the quantum realm also has something that works quite well already and that is quantum simulators. In a quantum simulator, at least one of the constituents behaves quantum mechanically. As with the classical simulators, the power of the quantum simulator derives from the fact that its computation is simply its natural evolution. The soap formed the minimal surface over the wires just because this is how soap films behave on wire constructions.

Likewise, the quantum simulator is designed such that the natural evolution of the system mimics a problem we would like to study. And because it behaves quantum mechanically, it is able to mimic other quantum systems much more efficiently than a classical simulator or computer could. Why don't we just study the original system? It might not be possible or a good idea. No one suggested instead of using MONIAC to instead raise taxes by 30% to see what happens, at least not very loudly.

Depending on the implementation of the simulator, a variety of different skills and techniques may be required to keep it operational or to perform operations and readout. In trapped ions this usually involves vacuum chambers, lasers of many different colours and intensities and microwave and radiowave sources and engineering. In superconducting qubit systems there are usually no lasers, but instead there is involved cryogenics to cool down to few Kelvins or even milli- and micro-Kelvin.

Such quantum simulators have already demonstrated computational capabilities that provide an improvement over classical computation by 10e80 or somewhat figuratively a computer containing every atom of the observable universe.

Some of the experiments in trapped ion quantum simulation such as Rainer Blatt's group in Innsbruck have reached the state where they are stable and reliable enough for chemists to 'order' the study of a certain chemical reaction that has eluded study as of yet.

So are we almost done?

The field of quantum simulation itself, just as quantum computation, is still far away from being the solution to all our problems. Pretend we had solved all technical challenges, quantum simulators would still be restricted to solve a very specific problem (or at least a somewhat broader class of problems). Say we also solved all problems in quantum computation that are implementation based. A quantum computer, when not used properly, is just a very expensive classical computer. You need the right algorithms to make use of the quantum capabilities, because the observation at the end reduces the qubit state to one bit of classical information. So you better make sure that 1 or 0 tells you something meaningful or it was all a huge waste of energy. Of course people are working on these and make neat tables with plenty of weird symbols in them.

But what does that mean for our original conundrum? Will we just bash into a wall where less and less computational power and bandwidth per person will limit our way of live? Some countries have already started two-class internet, after all! Or will we find a way around that?

It means we are on the way and we may find that in fact, the quantum world solves some if maybe not all of our problems. But with current wisdom, it doesn't look like quantum computation will ever run Call of Duty 26 any faster than the Intel Phantasmogasm 9 based on classical computation. It is also not likely to find a quantum computer in every household or even portable, what with the current qubits being in vacuum chambers or even in cryostats. It might be that we send requests such as “Factorize this number quickly” to a central computer somewhere and given the answer coming back we find that we can look at high definition cat videos while simultaneously solve mysteries around magnetism and the origin of of the universe. It is also comforting that for the time being, the Terminator will likely run out of memory before he can kill Sarah Connor.

Author: Christian Marciniak