Fixing errors without looking

An ordinary computer fixes errors by keeping three copies and taking a vote. That is out: a qubit cannot be copied, and reading it to compare would wreck it.

The way round, found in 1995, is to store one qubit's worth of information in the relationships between several qubits, and then measure only the relationships. You can ask 'are qubits 1 and 2 the same?' without learning what either one is. If they were the same and now they are not, one of them flipped, and asking a second question tells you which. Then you flip it back. The stored information was never read.

The surface code is the version the leading machines use. Picture a checkerboard. The qubits that hold the data sit on the white squares. The black squares are checker qubits whose only job is to ask their four neighbours whether they still agree. Run the checks over and over, feed the pattern of complaints to an ordinary computer, and it works out where the errors are.

The threshold theorem from 1997 says: if each part errs less than about one time in a hundred, a bigger checkerboard gives a more reliable stored qubit, and you can make the reliability as high as you like by making the board bigger. Above that rate, a bigger board is worse. For 25 years every machine was above the line. In December 2024 Google's Willow chip showed the error halving each time the board grew, from 3×3 to 5×5 to 7×7. That is the line, crossed.

The cost is the catch. One good stored qubit, called a logical qubit, takes a board of several hundred to a couple of thousand physical qubits at today's error rates. A useful machine wants a few thousand logical qubits. That multiplies to a few million physical ones. Nobody is close. Newer codes found in 2023 and 2024 cut the multiplier roughly tenfold, and that is where much of the research is.