# Explaining the upside and downside of D-Wave’s new quantum computer

D-Wave, a company based in British Columbia, has announced
a new version of its quantum annealer: the D-Wave 2000Q. As the name
suggests, the number of bits has increased from about 1,000 to just over
2,000. This is, for D-Wave, an important step on its roadmap to world
domination. D-Wave's approach is to increase the number of qubits come
hell, high water, or lack of quantumness.

Luckily, hell has stayed south of the border,
winter has prevented flooding, and the associated papers indicate that
their new board preserves the quantum behavior of the previous
generation. But under the hood, it appears that D-Wave has made some
pretty significant changes to scale up.

## Ice cold Ising models

The D-Wave computer is based on a process
called annealing. Annealing involves a series of magnets that are
arranged on a grid. The magnetic field of each magnet influences all the
other magnets—together, they flip orientation to arrange themselves to
minimize the amount of energy stored in the overall magnetic field. You
can use the orientation of the magnets to solve problems by controlling
how strongly the magnetic field from each magnet affects all the other
magnets.

To obtain a solution, you start with lots of
energy so the magnets can flip back and forth easily. As you slowly
cool, the flipping magnets settle as the overall field reaches lower and
lower energetic states, until you freeze the magnets into the lowest
energy state. After that, you read the orientation of each magnet, and
that is the solution to the problem. You may not believe me, but this
works really well—so well that it's modeled using ordinary computers
(where it is called simulated annealing) to solve a wide variety of
problems.

One issue with classical annealing is that the
grid of magnets can become trapped in a low-energy valley on the way to
the deep valley of the correct solution. Here, cooling becomes your
enemy, because the magnets need energy to jump above the energy valley, a
necessary step for them to find the even lower-energy solution on the
other side.

And this is where quantum mechanics plays a
role. A classical system has to have the energy to go over an energy
barrier, while quantum particles can simply

*go through*an energy barrier. This has several effects: it means that a quantum annealing process can escape valleys more efficiently, making it more likely to find the correct solution. You can also cool the magnets faster, knowing that as long as the barriers are manageable, quantum tunneling will keep you on track.
Most importantly, the physics that allows
tunneling also means that the quantum state of neighboring magnets may
spatially overlap with each other. As a result, they mix with each other
so that they can act collectively. An example: imagine that a group of
four neighboring magnets are in a state such that if one, two, or three
magnets flip, the energy goes up. But, if all four flip, then the energy
goes down. Individual tunneling cannot help here, as all four have to
flip at the same time. Classical physics plus tunneling makes this
highly unlikely. But if the magnets are in a collective quantum state,
this can occur with a much higher probability.

## Too many wires

While quantum annealing sounds pretty simple,
there is a hidden architectural challenge: you need a controllable
connection between every magnet for them to act collectively. In a grid
of four magnets, there are six connections; for 16 magnets, there are
120 connections. I don't even want to think about how many interconnects
a 2,000-qubit machine would require.

D-Wave has chosen to scale qubit numbers at
the expense of interconnectivity. And, the latest processor is no
different. Qubits are arranged on what is called a chimera graph.
Essentially, individual qubits are clustered
at three levels, which are illustrated in the diagram above. The first
level, which I'll call the inner node, is a group of four qubits
connected in a loop, so each qubit has two connections to neighbors. The
second level, which I'll call the outer node, is another set of four
qubits that are also connected in a loop. The inner and outer nodes are
connected to each other, with each qubit in the outer node connecting to
two in the inner one. These groupings are connected to neighboring
ones, with each qubit on the inner node connected to two qubits on each
of the nearest neighboring inner nodes.

This is all arranged in a 12×12 block, giving
1,152 logical qubits, with (though it is not explicitly said) the
remaining 880 qubits used to control coupling. There are not enough
qubits left to control the coupling between every connected qubit, so
I'd guess that there is a control qubit on the lines between neighboring
nodes but no control over the coupling within and between inner and
outer nodes.

Compared to the older D-Wave architecture, the
arrangement is different, but no sacrifices in connectivity have been
made. In fact, things are better. In the old system, each qubit had four
within-node connections and two between-node connections. This is
unchanged in the new architecture. However, connections between
next-to-nearest neighbors is improved. In the previous architecture, two
qubits that are on nodes diagonally next to each other are, at best,
three connections away from each other (at worst, they're five
connections apart). In the new system, any two qubits that are on a
diagonal to each other are only separated by three connections.

## Reaping the benefits

In a pair of papers,
D-Wave researchers have compared the new architecture to various
simulated annealers, including annealers that incorporate quantum
properties and make use of GPUs for additional speed up. The take-home
message that D-Wave wants you to hear is that this thing is a processing
beast, around 1,000 times faster than a normal computer. This is just a
comparison of the annealing time, though. The total time taken is only a
factor of 30 better, and it's dominated by the time it takes to
initialize the problem and read out the solution. These are also
just demonstration problems that are not directly applicable in
real-world applications.

The more important conclusion is that if you
compare the scaling of time-to-solution with problem size, the D-Wave
system scales in an identical manner to a

*quantum*simulated annealing algorithm. There has been some evidence of this before, but, the new architecture allows for bigger problems, which makes the scaling clearer.
A second problem that the D-Wave scientists
addressed was more subtle: often the ground state is not unique. Many
different arrangements of magnets can lead to the same energy, which
also happens to be the lowest possible energy. Any particular run with
this computer will only find a single ground state—does the processor
always find the same ground state, some limited distribution of them, or
does it sample them in an unbiased statistical fashion?

In several sets of experiments, D-Wave's
people show that the annealer samples in a relatively unbiased fashion.
What does this mean? Well, for many quantum problems—for instance,
determining the structure and properties of molecules—it is not enough
to find

*a*solution. You need to find all of them, and you need to know the barriers between these different solutions before you can understand the stability of each molecular structure.
We now know that the D-Wave annealer is not
inherently biased to find particular solutions. So, if such a problem
can be put on a D-Wave annealer, you can be reasonably confident of
finding a useful set of solutions.

In a final short white paper (PDF),
D-Wave compares power consumption. The company shows that, even when
you take into account the cost of cooling to below liquid helium
temperatures, they still get better performance per Watt than the best
supercomputers. Furthermore, because the circuits are actually
superconducting, scaling the number of qubits will not substantially
increase the power consumption. The main cost is holding the board at a
few milliKelvin; as long as the boards remain relatively compact, that
cost will not increase much.

## And now for the bad news

I am hypocritically worried on two fronts.
First, D-Wave's computers are starting to get large enough to be useful
for real-world problems. There is a substantial computational cost due
to the lack of interconnection, because problems must be rewritten to
cope with the limitations of the architecture. This limitation is severe
enough that not all problems can be rewritten to fit the architecture.
In other words, this is not a universal computer. I expect this means
that all of my favorite problems will remain untouched by D-Wave
computers, and that makes me sad.

Unfortunately, I think the architecture is
suitable for many problems that I wish would remain untouched. I
actually like my secure connection to my bank, and I am discomforted by
the fact that quantum computing appears to be getting here ahead of
alternative encryption algorithms. I know that if it wasn't D-Wave, it
would be someone else, but that thought is even less comforting.

*arXiV.org*, 2016, arXiv:1611.04528 (About the arXiv).

*arXiV.org*, 2017, arXiv:1701.04579 (About the arXiv).

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