Here is a nice shot of two D-Wave OneTM systems being tested in the lab!
I’ve been thinking about the BlackBox compiler recently and came up with a very interesting analogy to the way it works. There are actually lots of different ways to think about how BlackBox works, and we’ll post more of them over time, but here is a very high level and fun one.
The main way that you use BlackBox is to supply it with a classical function which computes the “goodness” of a given bitstring by returning a real number (the lower this number, the better the bitstring was).
Whatever your optimization problem is, you need to write a function that encodes your problem into a series of bits (x1, x2, x3…. xN) to be discovered, and which also computes how “good” a given bitstring (e.g. 0,1,1…0) is. When you pass such a function to Blackbox, the quantum compiler then repeatedly comes up with ideas for bitstrings, and using the information that your function supplies about how good its “guesses” are, it quickly converges on the best bitstring possible.
So using this approach the quantum processor behaves as a co-processor to a classical computing resource. The classical computing resources handles one part of the problem (computing the goodness of a given bitstring), and the quantum computer handles the other (suggesting bitstrings). I realized that this is described very nicely by the two computers playing 20 questions with one another.
The quantum computer suggests creative solutions to a problem, and then the classical computer is used to give feedback on how good the suggested solution is. Using this feedback, BlackBox will intelligently suggest a new solution. So in the example above, Blackbox knows NOT to make the next question “Is it a carrot?”
There is actually a deep philosophical point here. One of the pieces that is missing in the puzzle of artificial intelligence is how to make algorithms and programs more creative. I have always been an advocate of using quantum computing to power AI, but we now start to see concrete ways in which it could really start to address some of the elusive problems that crop up when trying to build intelligent machines.
At D-Wave, we have been starting some initial explorations in the areas of machine creativity and machine dreams, but it is early days and the pieces are only just starting to fall into place.
I was wondering if you could use the QC to actually play 20 questions for real. This is quite a fun application idea. If anyone has any suggestions for how to craft 20 questions into an objective function, let me know. My first two thoughts were to do something with Wordnet and NLTK. You could try either a pattern matching or a machine learning version of ‘mining’ wordnet for the right answer. This project would be a little Watson-esque in flavour.
Here is a video showing how some of the parts of a D-Wave Rainier processor go together to create the fabric of the quantum computer.
The animation shows how the processor is made up of 128 qubits, 352 couplers and nearly 24,000 Josephson junctions. The qubits are arranged in a tiling pattern to allow them to connect to one another.
There are two new tutorials on the website, complete with code snippets! Click on the images to go to the tutorial pages on the developer portal:
This tutorial (above) describes how to solve Weighted Maximum Independent Set (WMIS) problems using the hardware. Finding the Maximum Independent Set of a bunch of connected variables can be very useful. At a high level, the MIS it gives us information about the largest number of ‘things’ that can be achieved from a set when lots of those ‘things’ have conflicting requirements. In the tutorial, an example is given of scheduling events for a sports team, but you can imagine all sorts of variants: Train timetabling to improve services, assigning patients to surgeons to maximize the throughput of vital operations and minimize waiting lists, adjusting variable speed limits on motorways to reduce traffic jams during periods of congestion, etc etc.
This tutorial (above) describes how to find Maximum Common Subgraphs given two graphs. The example given in this tutorial is in molecule matching. Looking for areas where sub-structures in molecules are very similar can give us information about how such molecules behave. This is just one simple example of MCS. You can also imagine the same technique being applied to social networks to look for matches between the structuring of social groups. This technique could be used for improving ad placement or even for detecting crime rings.
These two tutorials are closely linked – as finding the MCS involves finding the MIS as part of the process. There are also lots of interesting applications of both these methods in graph and number theory.
If anyone would like to implement WMIS or MCS to solve any of the problem ideas mentioned in this post, please feel free!
The next generation of D-Wave’s technology is called Vesuvius, and it’s going to be a very interesting processor. The testing and development of this new generation of quantum processor is going well. In the meantime, here are some beautiful images of Vesuvius!
Above: An entire wafer of Vesuvius processors after the full fabrication process has completed.
Above: Photographing the wafer from a different angle allows more of the structure to be seen. Exercise for the reader: Estimate the number of qubits in this image
Above: A slightly closer view of part of the wafer. The small scale of the structures (<1um) produces a diffraction grating effect (like you see on the underside of a CD) resulting in a beautiful spectrum of colours reflecting from the wafer surface.
Above: A different angle of shot produces different colours and allows different areas of the circuitry to become visible.
Above: A close-up image of a single Vesuvius processor on the wafer. The white square seen to the right of the image contains the main ‘fabric’ of 512 connected qubits.
Above: An image of a processor wire-bonded to the chip carrier, ready to be installed into the computer system. The wires carry the signals to the quantum components and associated circuitry on the chip.
Above: A larger view of the bonded Vesuvius processor. More of the chip packaging is now also visible in the image.
Above: The full chip packaging is visible, complete with wafer.
So as part of learning how to become a quantum ninja and program the D-Wave One, it is important to understand the problem that the machine is designed to solve. The D-Wave machine is designed to find the minimum value of a particular mathematical expression which I can write down in one line:
As people tend to be put off by mathematical equations in blogposts, I decided to augment it with a picture of a cute cat. However, unless you are very mathematically inclined (like kitty), it might not be intuitive what minimizing this expression actually means, why it is important, or how quantum computing helps. So I’m going to try to answer those three questions in this post.
1.) What does the cat’s expression mean?
The machine is designed to solve discrete optimization problems. What is a discrete optimization problem? It is one where you are trying to find the best settings for a bunch of switches. Here’s a graphical example of what is going on. Let’s imagine that our switches are light switches which each have a ‘bias value’ (a number) associated with them, and they can each be set either ON or OFF:
The light switch game
The game that we must play is to set all the switches into the right configuration. What is the right configuration? It is the one where when we set each of the switches to either ON or OFF (where ON = +1 and OFF = -1) and then we add up all the switches’ bias values multiplied by their settings, we get the lowest answer. This is where the first term in the cat’s expression comes from. The bias values are called h’s and the switch settings are called s’s.
So depending upon which switches we set to +1 and which we set to -1, we will get a different score overall. You can try this game. Hopefully you’ll find it easy because there’s a simple rule to winning:
We find that if we set all the switches with positive biases to OFF and all the switches with negative biases to ON and add up the result then we get the lowest overall value. Easy, right? I can give you as many switches as I want with many different bias values and you just look at each one in turn and flip it either ON or OFF accordingly.
OK, let’s make it harder. So now imagine that many of the pairs of switches have an additional rule, one which involves considering PAIRS of switches in addition to just individual switches… we add a new bias value (called J) which we multiply by BOTH the switch settings that connect to it, and we add the resulting value we get from each pair of switches to our overall number too. Still, all we have to do is decide whether each switch should be ON or OFF subject to this new rule.
But now it is much, much harder to decide whether a switch should be ON or OFF, because its neighbours affect it. Even with the simple example shown with 2 switches in the figure above, you can’t just follow the rule of setting them to be the opposite sign to their bias value anymore (try it!). With a complex web of switches having many neighbours, it quickly becomes very frustrating to try and find the right combination to give you the lowest value overall.
2.) It’s a math expression – who cares?
We didn’t build a machine to play a strange masochistic light switch game. The concept of finding a good configuration of binary variables (switches) in this way lies at the heart of many problems that are encountered in everyday applications. A few are shown in figure below (click to expand):
Even the idea of doing science itself is an optimization problem (you are trying to find the best ‘configuration’ of terms contributing to a scientific equation which matches our real world observations).
3.) How does quantum mechanics help?
With a couple of switches you can just try every combination of ON’s and OFF’s, there are only four possibilities: [ON ON], [ON OFF], [OFF ON] or [OFF OFF]. But as you add more and more switches, the number of possible ways that the switches can be set grows exponentially:
You can start to see why the game isn’t much fun anymore. In fact it is even difficult for our most powerful supercomputers. Being able to store all those possible configurations in memory, and moving them around inside conventional processors to calculate if our guess is right takes a very, very long time. With only 500 switches, there isn’t enough time in the Universe to check all the configurations.
Quantum mechanics can give us a helping hand with this problem. The fundamental power of a quantum computer comes from the idea that you can put bits of information into a superposition of states. Which means that using a quantum computer, our light switches can be ON and OFF at the same time:
Now lets consider the same bunch of switches as before, but now held in a quantum computer’s memory:
Because all the light switches are on and off at the same time, we know that the correct answer (correct ON/OFF settings for each switch) is represented in there somewhere… it is just currently hidden from us.
What the D-Wave quantum computer allows you to do is take this ‘quantum representation’ of your switches and extract the configuration of ONs and OFFs with the lowest value.
Here’s how you do this:
You start with the system in its quantum superposition as described above, and you slowly adjust the quantum computer to turn off the quantum superposition effect. At the same time, you slowly turn up all those bias values (the h and J’s from earlier). As this is performed, you allow the switches to slowly drop out of the superposition and choose one classical state, either ON or OFF. At the end, each switch MUST have chosen to be either ON or OFF. The quantum mechanics working inside the computer helps the light switches settle into the right states to give the lowest overall value when you add them all up at the end. Even though there are 2^N possible configurations it could have ended up in, it finds the lowest one, winning the light switch game.