Quantum Computing: The Simple Math that Makes it Work

How many times did you read the term “superposition”, “entanglement”, and “decoherence”? The more you read, the greater the mystery. Do you get the suspicion that quantum mavens enjoy your bewilderment?

The naked truth is that quantum physics, unlike Newtonian physics, is a humble one. Newton told us what is going on. A quantum physicist says: I am absolutely clueless about what is going on. I have past measurements, and all I can do is to assign probabilities to possible future measurements. What happened between measurements is a persistent mystery, used to confuse the casual reader.

Yes, quantum computing is probability calculus. But with a twist. Casinos use probability calculus in order to stay in business, the weatherman uses probability calculus to forecast the weather, investors pick stock based on probability. So does the quantum physicist, only that they use a simple mathematical fact:

While probability cannot be negative, its square root can!

Probability is a real number between 0 and 100%. Negative probability is meaningless. However, the square root of probability p, call it q, can be positive or negative because the square of a negative number is a positive number. If p = 1%, then the square root of p may be +10%, or -10%. Quantum computing handles square roots of probabilities thereby allowing probabilities to negate each other (which cannot happen with all numbers positive). The computational richness afforded by this twist is then applied to computational challenges. A quantum computer will give you a probability distribution over all possible outcomes. We start with a flat distribution — all possible outcomes are of equal likelihood, then we throw in everything we know until this probability distribution favors one outcome, which we then announce it as the right answer.

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