When can Quantum Annealing win

Posted by Hartmut Neven, Director of Engineering

During the last two years, the Google Quantum AI team has made progress in understanding the physics governing quantum annealers. We recently applied these new insights to construct proof-of-principle optimization problems and programmed these into the D-Wave 2X quantum annealer that Google operates jointly with NASA. The problems were designed to demonstrate that quantum annealing can offer runtime advantages for hard optimization problems characterized by rugged energy landscapes.

We found that for problem instances involving nearly 1000 binary variables, quantum annealing significantly outperforms its classical counterpart, simulated annealing. It is more than 10⁸ times faster than simulated annealing running on a single core. We also compared the quantum hardware to another algorithm called Quantum Monte Carlo. This is a method designed to emulate the behavior of quantum systems, but it runs on conventional processors. While the scaling with size between these two methods is comparable, they are again separated by a large factor sometimes as high as 10⁸.

Time to find the optimal solution with 99% probability for different problem sizes. We compare Simulated Annealing (SA), Quantum Monte Carlo (QMC) and D-Wave 2X. Shown are the 50, 75 and 85 percentiles over a set of 100 instances. We observed a speedup of many orders of magnitude for the D-Wave 2X quantum annealer for this optimization problem characterized by rugged energy landscapes. For such problems quantum tunneling is a useful computational resource to traverse tall and narrow energy barriers.

While these results are intriguing and very encouraging, there is more work ahead to turn quantum enhanced optimization into a practical technology. The design of next generation annealers must facilitate the embedding of problems of practical relevance. For instance, we would like to increase the density and control precision of the connections between the qubits as well as their coherence. Another enhancement we wish to engineer is to support the representation not only of quadratic optimization, but of higher order optimization as well. This necessitates that not only pairs of qubits can interact directly but also larger sets of qubits. Our quantum hardware group is working on these improvements which will make it easier for users to input hard optimization problems. For higher-order optimization problems, rugged energy landscapes will become typical. Problems with such landscapes stand to benefit from quantum optimization because quantum tunneling makes it easier to traverse tall and narrow energy barriers.

We should note that there are algorithms, such as techniques based on cluster finding, that can exploit the sparse qubit connectivity in the current generation of D-Wave processors and still solve our proof-of-principle problems faster than the current quantum hardware. But due to the denser connectivity of next generation annealers, we expect those methods will become ineffective. Also, in our experience we find that lean stochastic local search techniques such as simulated annealing are often the most competitive for hard problems with little structure to exploit. Therefore, we regard simulated annealing as a generic classical competition that quantum annealing needs to beat. We are optimistic that the significant runtime gains we have found will carry over to commercially relevant problems as they occur in tasks relevant to machine intelligence.

For details please refer to http://arxiv.org/abs/1512.02206.

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POP mp3 is downloaded when using facebook chat

This is nothing but the new message sound. It is not a virus or bug.
To disable it, just Click on options and Un-check "Play sound for new messages"
Thats it, now enjoy chatting.

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Vital Considerations To Make When Choosing Recovery Data Software

By Cornelia White

Losing data can be very inconveniencing especially if you were working on an important project. When faces with such a situation, you could choose the option of contacting a data recovery center. Alternatively, one can explore the more convenient option of shopping for recovery data software online. A good number of people with computers store crucial information in computer disks, USB drives or external hard disks. It is best to know the best options you could go for since you never know when the need for such programs would arise.

It would not be easy for you to make a good research when your files are already lost and you need them urgently. This means that you should protect your interests and work by ensuring that you begin research on this when you have no pressure. Start by talking to some of your friends or people in your circles, they may know a thing or two about such software and could help you make a good choice.

The opinions of other people does matter a lot. In any case, you will not want to buy something which everyone claims is ineffective. Take time to hunt for the reviews of a program before deciding to use it. What you should know is that the outcome of the recovery process would highly depend on the kind of program you use.

A good program will be well reviewed, dependable, user-friendly and efficient. Read the user manual provided and scrutinize every detail that offers information regarding the proper use of specific software. Point out any complexities found before you acquire the program. Usually, it does not make sense to buy something that is too complicated for your understanding.

If you know a little about computer data storage in order to be able to use a program properly. It is best to choose programs that have a wizard interface. This makes it easier for most people to understand how to use even complex programs. In case you cannot call yourself a guru in computer matters, you should at all costs avoid getting a program that is fashioned to suit only those with strong command of professional processor operations.

The aspects that lead to loss of data differ from one to another. The right program for you must provide a reasonable range of recovery modes. This means that you would be able to pick the mode that best suits your particular situation. You can confidently say that a program is not good if it has only one recovery mode. Ensure that you choose the programs of providers who have a well-established technical support and customer support department.

The basic aspect to consider before making a choice is the kind of results that would be produced. Your finding should put you in a position to judge if a program is good. Reliable software will be able to recover files. It will also ensure that the recovered files are correct.

When choosing recovery data software you would need to ensure that you could get a sneak preview of a file before recovering it. Some programs are designed to ensure that a client pays before copies of the lost data can be copied out. Such programs are good provided they support file preview.

About the Author:

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