Running complicated algorithms on quantum computing hardware requires the use of logical qubits, where collections of hardware qubits are linked together in a way that allows errors to be detected and corrected. In general, the more hardware qubits you assign to each logical qubit, the better the chances of identifying errors. However, because the hardware qubits are error-prone, adding more qubits also increases the chances of errors occurring. If the hardware error rate is too high, increasing the size of the logical qubit will only make things worse.
Fortunately, several companies have demonstrated hardware where the error rate is not too high. Several demonstrations show that logical qubits have broken even, with adding more qubits improving performance. The problem is that the improvement isn’t very dramatic. To reduce error rates to the level we need to run complex algorithms, we would have to add a completely impractical number of qubits to each logical qubit.
On Monday, Quantinuum announced that its current generation of hardware is capable of scaling well beyond breakeven. Each increase in the size of logical qubits improved some performance measures by a factor of more than 10.
Error correction codes and scaling
To understand the results, we need to take a slight detour through the ideas of error correction. A logical qubit consists of a set of qubits that store data and another set used for measurements, all linked together. There are different error-correction “codes,” each with a different geometry of entangled connections between the qubits that compose it. During operation, measurements of the corresponding qubits produce so-called “syndrome data,” which can be interpreted as an indication of whether an error has occurred in the logical qubit, as well as where and what type it is.
Depending on their geometry, error codes have a number of important properties: how many hardware qubits are required for them to function, how many individual logical qubits they contain, and something called spacing. This is a rough measure of how many errors can occur simultaneously before the logical qubit fails.
