Mastering Quantum Computing with IBM QX by Dr. Christine Corbett Moran;

Author:Dr. Christine Corbett Moran; [Dr. Christine Corbett Moran]
Language: eng
Format: epub
Tags: COM072000 - COMPUTERS / Computer Simulation, COM044000 - COMPUTERS / Neural Networks, COM004000 - COMPUTERS / Intelligence (AI) and Semantics
Publisher: Packt Publishing
Published: 2019-01-31T15:01:10+00:00

Now, imagine the government gets together and implements new legislation in which there are thirty different possible documents, which means 230 = 1,073,741,824 possible combinations and which the formula to determine whether a set of documents is valid is long and difficult but still takes only a few minutes per document set for the document checker to check. After a few days on the job with the new legislation, the document checker checks a few hundred people's documents per day, but no one's documents are valid. Their boss is upset, and both of them begin to suspect there is a flaw in the legislation, and that perhaps there is no combination of valid documents.

The boss orders the document checker to see if there are any valid combinations. There seems to be fewer than in the last scenario, so if they could just list the few combinations that are valid, they could save everyone time. This could take a while, but luckily the document checker has a computer program. In the worst case, the computer program will need to go through every one of the 1,073,741,824 possibilities for combinations of documents to see if each is valid before reaching the end and giving up. The document checker thinks that if we study the formula, we can see whether there might be vast classes of possibilities they could rule out all at once, saving the code some time.

Before we can get to running the code, we get interference. The government got wind of the boss and the document checker's plan to discredit them and so no longer publish the formula, which they claim could be taken advantage of if widely known. Instead, each time the document checker wants to check a combination of documents, they must call a toll free number and wait on hold, tell the operator the combination of documents, and the operator will say yes or no. It takes 4 minutes to check each combination of documents, so the document checker can still reach their target of 100 documents checked per day, but it would now take more than 30,000 years working at 40 hours a week for the document checker to be able to prove the government wrong in this situation; this example is admittedly contrived to illustrate what a checker function such as documents_ok could be used for. The document checker now suspects there is no possible combination of documents that are valid, but there is no way to prove that.

In the quantum computing literature, a function that you don't have access to which can check whether a given input is the correct input is known as an oracle function. I won't use this terminology but it might help when interpreting other writings on the subject.

The process of figuring out whether any possible combination of Boolean variables could satisfy a Boolean expression is known as the Boolean satisfiability problem or SAT. In this section, we will see that a quantum computer could let the document checker prove

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