Yes in the sense that it uses quantum properties to perform computations, but no in the more general case since it is not a Turing machine (i.e. universal computer).
This answer is somewhat complicated by the fact that what the general public thinks of as a computer and what computer scientists formally define as a Turing machine. Turing machines are interesting from a mathematical standpoint since any computer algorithm can be run on a Turning machine and Turing machines can simulate one another which gives rise to the concept of Turing completeness.
The quantum equivalent to a conventional Turing machine (i.e. a desktop computer) requires the use of quantum circuits that allow for general algorithms to be run on it. In keeping with Turing completeness, conventional computers can actually simulate quantum computers that make use of quantum circuits.
So with that in mind we can now turn to the D-Wave device for closer examination. D-Wave Systems own documentation for developers tells us the following:
The processor in the D-Wave One – codenamed Rainier – is designed to
perform a single mathematical operation called discrete optimization.
Rainier solves optimization problems using quantum annealing (QA),
which is a class of problem solving approaches that use quantum
effects to help get better solutions, faster.
Right off the bat we know that the D-Wave is not going to be Turing complete since it can only perform a single mathematical operations which means that it is not a quantum computer in the general sense; however, what about the specific case?
When first introduced there was quite a bit of controversy that D-Wave was not taking advantage of quantum effects to actually solve problems. However, this partly resolved with their 2011 publication of "Quantum annealing with manufactured spins" in Nature which contains the following point of interest in the abstract,
Here we use quantum annealing to find the ground state of an
artificial Ising spin system comprising an array of eight
superconducting flux quantum bits with programmable spin–spin
couplings. We observe a clear signature of quantum annealing,
distinguishable from classical thermal annealing through the
temperature dependence of the time at which the system dynamics
freezes. Our implementation can be configured in situ to realize a
wide variety of different spin networks, each of which can be
monitored as it moves towards a low-energy configuration
The paper is quite interesting but the mathematics can be quite heavy at times as well though. The key point of the paper is summarized in the conclusion,
This brings us to our main conclusion: a programmable artificial spin
system manufactured as an integrated circuit can be used to implement
a quantum algorithm. The experiments presented here constitute a step
between understanding single-qubit annealing and understanding the
multi-qubit processes that could be used to find low-energy
configurations in a realistic adiabatic quantum processor. In addition
to its problem-solving potential, a system such as this also provides
an interesting test bed for investigating the physics of interacting
quantum spins, and is an important step in an ongoing investigation
into much more complex spin systems realized using this type of
architecture. Although our manufactured spin system is not yet a
universal quantum computer, by adding a new type of coupler between
the qubits, universal quantum computation would become possible.
In short, the paper explains the implementation of a means of doing adiabatic quantum computation. This paper was part of what ultimately lead some of D-Waves critics to back off their previous positions and look more favorably on the company. This in turn has lead to a general warming of the scientific communities options towards the company.
This position that the D-Wave is in fact using quantum effects was further reinforced by the University of Southern California who in 2013 released an article validating the use of quantum effects in the processor,
“Our work seems to show that, from a purely physical point of view,
quantum effects play a functional role in information processing in
the D-Wave processor,” said Sergio Boixo, first author of the research
paper, who conducted the research while he was a computer scientist at
ISI and research assistant professor at USC Viterbi
A 2013 pre-print article up titled "Quantum annealing with more than one hundred qubits" also raises a very interesting point,
Considering the pure annealing time, the performance for typical
(median) instances matches that of a highly optimised classical
annealing code on a high-end Intel CPU.
Meaning that as of right now, there might not be much advantage in using their device over a conventional computer. However, they go on to note that,
Quantum speedup can then be detected by comparing the scaling results
of the simulated classical and quantum annealers to experiments, as we
discuss in detail in the supplementary material. Going to even larger
problem sizes we soon approach the limits of classical computers.
Optimistically extrapolating using the observed scaling, the median
time to find the best solution for our test problem will increase
from milliseconds to minutes for 2048 variables, and months for 4096
variables, and the scaling might be much worse if fat tailed
distributions start to dominate, as we had previously observed for
other Monte Carlo algorithms [28, 29]. A quantum annealer showing
better scaling than classical algorithms for these problem sizes would
be an exciting breakthrough, validating the potential of quantum
information processing to outperform its classical counterpart.
Meaning that they still feel that for larger data sets their device is likely to be a superior performer over a standard computer for these types of problems.
So to summarize, in the general sense of the D-Wave One being a Turing machine, it is not which means that it is not a quantum computer in the strictest sense of the meaning. However, in the more general sense that the D-Wave One is using quantum effects to perform calculations, the answer appears to be yes.