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Why 15 = 5x3 is a major quantum breakthrough

Researchers at the University of California Santa Barbara have been working on a method of computer processing that is orders of magnitude faster than what we currently have available.

They are using quantum computing to calculate a number’s prime factors, specifically factoring 15 into 3 and 5. They wrote about it in Nature Physics.

The researchers, led by Erik Lucero, built a quantum processor that factored the number 15 some 150,000 times, and got the right answer 48 percent of the time, according to an announcement from UC Santa Barbara. That might not sound like much, but it’s a breakthrough for quantum computing, representing the first time a solid-state quantum processor had successfully done the math on prime factors, the researchers said.


Related story:

IBM achieves quantum computing milestone


Why prime factors? Well, finding the list of prime numbers that multiply together to make a certain number is one of the most basic functions of mathematics, and the one that consumes the most processing time by far. Even when using the best classical algorithm out there, it would take a conventional computer to find the prime factors of a 600-digit number longer than the age of the universe.

In 1994 a mathematician by the name of Peter Shor developed an algorithm that would considerably cut the time to find prime factors of extremely large numbers. The basic idea centers on reducing a number until it is non-even and is the product of two different numbers. But then, modular arithmetic comes in and it goes beyond simple explanation.

To implement this, you would need a quantum computer, which is about as hard to wrap your head around as Shor’s algorithm. Where a conventional computer stores data in bits, which can either be one or zero, a quantum computer has “qubits,” which can be one, zero, or any quantum superposition of those. See? If your brain hasn’t exploded yet, feel free to learn more.

Suffice to say that a quantum computer running Shor’s Algorithm could find the prime factors of that same 600-digit number in a matter of hours.

The one area where this would most heavily impact any agency is security. Right now, secure connections and transmissions use encryption to keep data from being seen by the wrong sets of eyes. Encryption such as the Secure Hash Algorithms, which are government standards, can use numbers as large as the example above to encode sensitive data, and what makes it work is that it would take far too long for a conventional computer to crack.

But if quantum computers became practical, all of that would be blown out of the water. A new order of encryption would be needed to protect data. Fortunately, people have already theorized quantum cryptography, which will keep pace should computing power should shift into this higher gear.

But this current experiment in Santa Barbara used only nine quantum elements, which is much less than the millions that would be needed to factor larger numbers. So our current encryption methods are just as safe as they’ve ever been.

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