Quantum Algorithms Conquer a New Kind of Problem

A mathematician figured out how to make a quantum computer work. A machine based on the rules of quantum mechanics could break a large number into its prime factors, a task so difficult for a classical computer that it forms the basis for much of today's internet security.

There was a surge of hope. Researchers thought that we would be able to solve a lot of different problems with the help of quantum technology.

Progress slowed down. The trajectory has been a bit of a bummer. People were excited about the fact that we were going to get a lot of other amazing programs. I don't think so. Dramatic speedups were only discovered for a single, narrow class of problems from within a standard set called NP.

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For a long time, that was the case. A quantum computer should be able to solve a classical problem in a fraction of the time. The inputs are calculated to a complicated mathematical process. The first in a new frontier of many others has yet to be determined.

A computer scientist at the Massachusetts Institute of Technology says there is a sense of excitement. Many people are thinking about what else is out there.

Computer scientists look at mathematical models that represent quantum computers. They imagine a model of a computer and an oracle together. Like a mathematical function or computer program, oracles take in an input and spit out a preset output. If the input falls within a certain random range, they might have a random behavior, outputting "yes" and "no" if it doesn't. They could be periodic, so that an input between 1 to 10 returns "yes", 11 to 20 returns "no", 21 to 30 returns "yes", and so on.

If you have a periodic oracle, you don't know the period. You can't do anything about it, just feed it numbers and see what it does. How fast could a computer find the time? Daniel Simon, then at the University of Montreal, found a way to calculate the answer to a closely related problem in less than a second.

Simon was able to figure out one of the first hints of quantum computers' superiority. His paper was rejected when he submitted it. Peter Shor was a junior member of the conference's program committee and he was interested in the paper. The period of an oracle can be calculated using Simon's algorithm, if it has one. He was able to adapt the formula to solve an equation that behaves like a periodic oracle.

It was the first time that a result was historic. It's not possible to reduce gigantic numbers into their prime factors using a classical algorithm. The years that followed saw the discovery of other efficient quantum algorithms. There was no quantum advantage on any NP problem that wasn't periodic.

Two computer scientists made an observation about the lack of progress. Proofs of quantum advantage depended on oracles that had some kind of random structure. They thought there couldn't be dramatic speedups on NP problems that weren't structured. There was no exception.

The powers of quantum computers were bound by their hypothesis. There were no dramatic speedups for certain types of NP problems. The problem of figuring out more specific, quantitative answers didn't apply to the conjecture.