Simulating Physics with Computers

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   A quantum computer does not ‘try every answer at once’: it arranges probability waves so that wrong answers cancel and the right one is reinforced, like the bands in the double-slit experiment — which works only for a few kinds of problems.

   Simulating Physics with Computers · 1982

   A quantum computer does not try every answer at once; it makes the wrong answers cancel each other out.

   An ordinary bit is like a coin lying on a table: heads or tails, 0 or 1. A qubit is more like the electron in the double-slit experiment. Until it is measured, it is described not by a single answer but by two ‘waves’, one for each possible result. These waves can add up, like waves meeting in step, or cancel, like waves meeting crest to trough. When you measure it, the qubit gives a single answer, 0 or 1, at random, with odds set by the waves. This is where the most common mistake comes from. People say a quantum computer ‘tries every option in parallel’. If that were all, at the end you would read one result at random — that is, nothing useful. The real trick is different: a quantum algorithm is a choreography of interference. Its steps are chosen so that the waves of the wrong paths cancel, like the dark bands on the screen, and those of the right answer reinforce, like the bright bands. That choreography can be written only for problems with a special structure. Two clear examples: simulating molecules and materials, which is exactly what Feynman proposed in 1981, and breaking large numbers into factors (Peter Shor's algorithm, 1994), which would break part of today's cryptography. That is why, in August 2024, the US standards institute NIST published the first ‘post-quantum’ cryptography standards. For most everyday things — email, games, spreadsheets, films — a quantum computer would bring nothing. The hard part is fragility. You saw in the lesson on observing that any leak of information to the environment destroys interference. For a qubit, that means errors. The fix is error correction: one ‘logical’ qubit is spread over many physical qubits that check one another. It works only if the physical qubits are good enough, below a certain threshold. In December 2024 Google's Willow chip showed convincingly, for the first time, that below the threshold a larger grid makes errors smaller, not larger. Breaking today's keys would need, by a 2025 estimate, close to a million qubits; today's chips have around a hundred.

   “Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.”

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