computer science//quantum computing//quantum superposition

Quantum superposition is the property of a quantum system to be in a weighted combination of several distinguishable states at once, with complex weights called amplitudes, and it is the resource a quantum computer works with: a register of \(n\) qubits can hold a superposition of all \(2^n\) bit strings simultaneously. It is a different thing from the superposition of interpretability, where a neural network packs more features than it has neurons into overlapping directions.

Quantum superposition is the property of a quantum system to be in a weighted combination of several distinguishable states at once, with complex weights called amplitudes, and it is the resource a quantum computer works with: a register of nnn qubits can hold a superposition of all 2n2^n2n bit strings simultaneously. It is a different thing from the superposition of interpretability, where a neural network packs more features than it has neurons into overlapping directions.

The common reading, that a quantum computer tries all answers in parallel, is half right and misleading. The register does evolve all the amplitudes at once, but a measurement returns one bit string, chosen at random with probability equal to the squared amplitude; reading a uniform superposition of a million candidates gives a random candidate, no better than guessing. What makes it useful is interference: amplitudes are complex numbers, so they can add or cancel like waves. An algorithm is a sequence of gates arranged so that the amplitudes of wrong answers cancel and those of right answers reinforce, and only then is the register measured.

Noise-cancelling headphones with arithmetic.

The headphones add a wave in antiphase so the engine drone vanishes and the voice remains; a quantum algorithm adds paths in antiphase so the wrong answers vanish and the right one remains to be heard.

Superposition alone gives no speedup; interference is what an algorithm engineers, and finding a problem with enough structure to arrange it is why so few quantum algorithms beat classical ones (quantum advantage).

Entanglement is superposition across several qubits that cannot be written as independent states of each one: measuring one fixes the statistics of the others. It is what lets amplitudes over many qubits interfere jointly.

Superposition is the first thing the environment destroys. Any interaction that leaks which state the system is in turns the superposition into an ordinary random mixture with no interference left (decoherence).