D-Wave implements quantum annealing, while Google has digitized adiabatic quantum computation.
D-Wave advertises their line of quantum computers as having thousands of qubits, though these systems are designed specifically for quadratic unconstrained binary optimization. More information about D-Wave's manufacturing process.
It is D-Wave's claim that: "It is best suited to tackling complex optimization problems that exist across many domains such as":
Sampling / Monte Carlo
Pattern recognition and anomaly detection
Software / hardware verification and validation
Bioinformatics / cancer research
D-Wave's QPU uses quantum annealing (QA), a metaheuristic for finding the global minimum of a given objective function over a given set of candidate solutions (candidate states), by a process using quantum fluctuations. Quantum annealing is used mainly for problems where the search space is discrete (combinatorial optimization problems) with many local minima; such as finding the ground state of a spin glass.
D-Wave's architecture differs from traditional quantum computers. It is not known to be polynomially equivalent to a universal quantum computer and, in particular, cannot execute Shor's algorithm because Shor's Algorithm is not a hillclimbing process. Shor's Algorithm requires a universal quantum computer. D-wave claims only to do quantum annealing.
Experimental quantum annealing: case study involving the graph isomorphism problem
Defects in Quantum Computers
Google's claim is: "The goal of the Google Quantum AI lab is to build a quantum computer that can be used to solve real-world problems. Our strategy is to explore near-term applications using systems that are forward compatible to a large-scale universal error-corrected quantum computer using linear array technology".
"State preservation by repetitive error detection in a superconducting quantum circuit"
"Digitized adiabatic quantum computing with a superconducting circuit"
Inaccurate layperson' explanation:
A Graphic Card has more Cores than a CPU.
GPUs are optimized for taking huge batches of data and performing the same operation over and over very quickly, unlike PC microprocessors, which tend to skip all over the place.
Architecturally, the CPU is composed of just few cores with lots of cache memory that can handle a few software threads at a time. In contrast, a GPU is composed of hundreds of cores that can handle thousands of threads simultaneously.
Technical, but not overly complicated, layperson's explanation:
Why is Google's new device newsworthy then? Is it better than D-Wave's machine in some respects? If so, how?
There are "Annealing QPUs" and "Universal QPUs" as explained above, an incomplete list is offered on Wikipedia's page: "List of Quantum Processors".
In quantum annealing, the strength of transverse field determines the quantum-mechanical probability to change the amplitudes of all states in parallel.
In the case of annealing a purely mathematical objective function, one may consider the variables in the problem to be classical degrees of freedom, and the cost functions to be the potential energy function (classical Hamiltonian). Moreover, it may be able to do this without the tight error controls needed to harness the quantum entanglement used in more traditional quantum algorithms.
That makes it easier to provide more qubits, but the kinds of problems they are able to solve is more limited than the qubits provided in a universal QPU.
In general the ground state of a Hamiltonian can be used to encode a wider variety of problems than NP (know QMA-complete problems), and so decision to focus on NP optimization problems has led to restrictions which prevent the device from being used for general purpose quantum computing (even if noise was not an issue).
There is an interesting subtlety as regards noise: If you add noise to the adiabatic algorithm, it degrades gracefully into one of the best classical algorithms for the same problem.
The adiabatic model can encode universal quantum computation, however the limitations of DWave's implementation means that specific machine cannot.
Google's universal QPU can solve a wider range of problems than D-Wave's QPU (in it's current implementation) if they can solve their decoherence problem.
In the case of Google's Bristlecone caution is warranted. Bristlecone is a scaled up version of a 9-qubit Google design that has failed to yield acceptable error rates for a commercially viable quantum system. In real-world settings, quantum processors must have a two-qubit error rate of less than 0.5 percent. According to Google, its best result has been a 0.6 percent error rate using its much smaller 9-qubit hardware.
The commercial success of quantum computing will require more than high qubit numbers. It will depend on quality qubits with low error rates and long-lasting circuit connectivity in a system with the ability to outperform classic computers in complex problem solving, i.e., “quantum supremacy”.
Google will use it's record number of more useful qubits to correct the error rate of those error prone qubits.
More qubits are needed to solve bigger problems and longer living (coherent) qubits to are needed to hold the information long enough for the quantum algorithm to run. IBM describes the problem as: "Quantum Volume: preferring fewer errors per qubit over more qubits", see also: What is the leading edge technology for creating a quantum computer with the fewest errors? .
Google plans to use Surface Codes to resolve this problem, for more info and a comparison to spin glass models see: "Quantum Computation with Topological Codes: from qubit to topological fault-tolerance".
IBM has a video titled: "A Beginner’s Guide to Quantum Computing" which explains quantum computing for laypersons in under 20 minutes.
Microsoft intends to take the wind from everyone's sails with the integration of Q# (Q sharp) into Visual Studio and some information about their Majorana fermion based qubits, and a great reduction in the error rate, in the months to come. See: "Majorana-based fermionic quantum computation". The will enable a system that uses less than 25% as many better qubits to accomplish the same amount of work as Google's qubits.
The website "The Next Platform" describes the current situation as: "Quantum Computing Enters 2018 Like it's 1968".