When the problems are solved -
A generating function has to be produced which encodes the problem as zeros and ones and produces a real number result (also zeros and ones). The mathematically and scientifically tricky part if figuring out the best way or at least one correct way to encode your problem as zeros and ones for an optimization solution.
The Dwave system then sets the qubits to encode the problems as zeros and ones and then the other qubits are set to the superposition of between zero and one. The field is slowly turned on. All of the connected qubits are trying to stay in the lowest ground state. The physics of the system is trying to keep the lowest ground state. If the system is quantum then it should go to the global minimum, where the best answer is. If it goes to a local minimum then it is not getting the best answer.
Looking at the qubits where the answer will be produced.
They have started out as between zero and one (basically 0.5).
The qubits are connected to the problem qubits and other answer qubits. The system is trying to get to the lowest energy ground state. So the many answer qubits move to zero or one based on keeping the ground state. If as the field is fully turned on they have stayed in the ground state then the correct answer is generated.
Dwave has several detailed tutorials about the hardware and tutorials about how to answer financial, machine learning and other problems.
Their protein folding problem solution has been published in the journal Science. The 81 qubits used in the published paper had the correct answers about 0.3 percent of the time. So they went from looking at 2 to power of 81 possible answers to looking at 300 answers. It is simple and fast for a regular computer to check 300 answers. Part of the coding is to have a checking function which verifies the quality of the answer. It is simple for classical computers to check and compare the quality of the result. Say you had factored prime numbers. It is tough to get the factored primes. Checking the result is just multiplying two answer numbers together and comparing the answer to the starting number.
For the past 8 years, the number of qubits on D-Wave's processors has been steadily doubling each year. This trend is expected to continue. To create processors with numbers of qubits up to around 10,000, the current fabrication process can simply be scaled to add more qubits in the same way that they are arranged currently. To go beyond ten-thousand into hundreds of thousands or millions of qubits will require major processor redesign, but there are certainly ways in which this can be achieved and it is not seen as a fundamental obstacle to improving the hardware.
In addition to doubling the qubit count every 12 months, further improvements are planned, which include increasing the precision of the programmable elements, reducing the footprint of the entire system, reducing the energy consumption of the system, and the inclusion of parallel cores (i.e. multiple processors) within a single refrigeration unit.
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