Interference: the main trick
Lesson 9 of 23 in the course “Quantum”. Free, with animations and a quiz.
You already use interference
Noise-cancelling headphones listen to the noise outside and play back the same wave, just flipped. Where the noise has a peak, the anti-noise has a trough, and together you get silence. That’s interference. Qubit amplitudes behave the same way: they have a sign, and a plus and a minus can cancel each other. The whole point of quantum computing is to create that silence for the wrong answers.
Why ordinary chances can’t do this
Ordinary probability is always positive. If two paths each give a quarter chance, the total is a half, and no second path can “take away” chance. Amplitudes are different: one can be plus a half, the other minus a half, and the sum is zero. Chance is the square of the amplitude, so zero amplitude means zero chance. That’s exactly how two H’s in a row erased the 1 in the gates lesson.
A four-step recipe
Almost all quantum algorithms follow one pattern. Step one: H gates create a superposition of all options. Step two: a special block, called an oracle, puts a minus on the options you want. Step three: more gates set up interference, and the pluses and minuses cancel the rest. Step four: measurement, and the right answer comes out with high probability. The art is designing steps two and three for a specific problem.
The first quantum win
In 1985 physicist David Deutsch came up with a toy problem. There’s a coin with two sides, and you need to know: are the sides the same, like a fake, or different, like a fair one? Classically you have to look at both sides. The quantum algorithm answers with one “look”: it looks at both sides in superposition, and interference immediately gives “same” or “different.” It’s not very useful, but it was the first proof that a quantum approach can be faster.
You can’t copy a qubit
A file can be copied as many times as you like. An unknown quantum state can’t: this was proved in 1982 by Wootters and Zurek, and independently by Dieks. It’s called the no-cloning theorem. The downside: a qubit has no “backup”, and you can’t peek at an intermediate result without spoiling the computation. The upside: a spy can’t secretly copy a quantum signal either, and quantum cryptography is built on that.
A race against time
Interference only works until the amplitudes get “smeared” by noise. The time a state holds up is called coherence time. For superconducting qubits it’s around a tenth of a millisecond; for ions it’s seconds or more. Ions seem to win outright, but superconducting gates are thousands of times faster, so over their lifetime they manage a comparable number of operations. That’s why people compare not time but the number of error-free steps.
Check yourself
- Why can a quantum computer “erase” a wrong answer while ordinary randomness can’t?
Correct answer: Amplitudes have a sign, and plus and minus cancel. Probabilities only add, but amplitudes can be negative. Plus and minus give zero, and the wrong answer’s chance disappears. - Can you back up a qubit in the middle of a computation?
Correct answer: No, an unknown state can’t be copied. The no-cloning theorem (1982) forbids copying an unknown quantum state. - Which comparison of qubits is fairer?
Correct answer: How many operations they manage without error. What matters is how many useful steps fit into the state’s lifetime. A slow long-lived qubit and a fast short-lived one can come out even.
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