"A quantum computer is based on manipulating the state of particles like electrons so that during the calculation, many different calculations are being performed at the same time, and only making a measurement at the end of the computation."

That is the succinct definition of quantum computing offered by Lawrence Krauss, a theoretical physicist and the author of The Physics of Star Trek and A Universe from Nothing, in the video below. 

So what would make a quantum computer so powerful is the ability to do many computations at same time. But achieving this is easier said than done. After all, as Krauss points out, we don’t behave quantum mechanically:

You want to make this macroscopic object, you want to keep it behaving quantum mechanically which means isolating it very carefully from, within itself, all the interactions and the outside world.  And that’s the hard part, Is isolating things enough to maintain this what's called quantum coherence.  And that’s the challenge and it’s a huge challenge.

And yet, the potential reward is as great as the challenge. "Once you can engineer materials on a scale where quantum mechanical properties are important," Krauss says, "a whole new world of phenomenon open up to you."

Watch here:

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